Class 10 Physics – Chapter 16: Current Electricity

Board: Federal Board (FBISE)

Multiple Choice Questions (MCQs)

1. Ampere-hour (Ah) is the unit of:

A. Electric current
B. Charge
C. Energy
D. Resistance

Correct Answer: B. Charge

2. Which of the following is a non-ohmic device?

A. Copper wire
B. Carbon resistor
C. Diode
D. All of these

Correct Answer: C. Diode

3. Electric current is measured using:

A. Ammeter
B. Voltmeter
C. Ohmmeter
D. Meter rod

Correct Answer: A. Ammeter

4. Voltmeter measures:

A. Potential difference
B. Electric current
C. Resistance
D. Resistivity

Correct Answer: A. Potential difference

5. If 3 A of current flows for 2 minutes, the amount of charge crossing the cross-section of a conductor will be:

A. 3 C
B. 6 C
C. 60 C
D. 360 C

Correct Answer: D. 360 C

6. A current of 1 mA is passing through a wire. The number of electrons passing through a point in the wire in 10 seconds is:

A. \(6.25\times10^{15}\)
B. \(6.25\times10^{16}\)
C. \(6.25\times10^{17}\)
D. \(6.25\times10^{18}\)

Correct Answer: A. \(6.25\times10^{16}\)

7. Resistance of a material always decreases when:

A. Its temperature increases
B. Its temperature decreases
C. Number of free electrons increases
D. Number of free electrons decreases

Correct Answer: C. Number of free electrons increases

8. The resistance of a metallic conductor varies inversely as:

A. Area of cross-section
B. Length
C. Temperature
D. All of these

Correct Answer: A. Area of cross-section

9. Directions of actual current and conventional current are:

A. Same
B. Opposite to each other
C. Perpendicular to each other
D. None of these

Correct Answer: B. Opposite to each other

10. As the temperature of a semiconductor increases, its resistance:

A. Increases
B. Decreases
C. Remains constant
D. Becomes zero

Correct Answer: B. Decreases

11. The SI unit of temperature coefficient of resistance (\(\alpha\)) is:

A. K
B. K\(^{-1}\)
C. \(\Omega\cdot K\)
D. \(\Omega/K\)

Correct Answer: B. K\(^{-1}\)

12. By increasing temperature, the resistivity of semiconductors:

A. Increases
B. Decreases
C. Remains constant
D. First increases then decreases

Correct Answer: B. Decreases

Constructed Response Questions

Question 1: Draw connections so that the EMF sources given in the figure become in series and parallel.

1. Series Connection

To connect four cells (\(E_1,E_2,E_3,E_4\)) in series:

• Connect the positive terminal (+) of \(E_1\) to the circuit’s positive end.

• Connect the negative terminal (−) of \(E_1\) to the positive terminal (+) of \(E_2\).

• Connect the negative terminal (−) of \(E_2\) to the positive terminal (+) of \(E_3\).

• Connect the negative terminal (−) of \(E_3\) to the positive terminal (+) of \(E_4\).

• Connect the negative terminal (−) of \(E_4\) to the circuit’s negative end.

Total EMF:

2. Parallel Connection

To connect four cells (\(E_1,E_2,E_3,E_4\)) in parallel:

• Connect all positive terminals (+) of \(E_1,E_2,E_3\), and \(E_4\) together to a common positive node.

• Connect all negative terminals (−) of \(E_1,E_2,E_3\), and \(E_4\) together to a common negative node.

Total EMF:

This applies when all cells are identical.

Question 2: Compare and contrast the roles of ammeters and voltmeters in electrical circuits. Include a discussion on how each instrument measures different electrical properties.

Comparison and Contrast Table

Detailed Discussion on Measurement

1. How an Ammeter Measures Current

An ammeter measures the rate of flow of electric charge through a circuit element. Since it is connected in series, the full current flowing through the branch passes through the ammeter.

Its extremely low internal resistance ensures that it does not produce a significant potential drop or restrict current flow, giving an accurate current reading.

2. How a Voltmeter Measures Potential Difference

A voltmeter measures the energy difference per unit charge between two distinct points in a circuit.

Since it is connected in parallel, it measures the voltage drop across the component. Its extremely high internal resistance prevents significant current from diverting into the voltmeter, leaving the main circuit operation largely unaffected.

Short Response Questions

1. Why is copper preferred over silver for household wiring, considering cost, conductivity, and durability?

Although silver has slightly higher electrical conductivity than copper, copper is drastically cheaper and more abundant. Additionally, copper offers excellent mechanical durability, flexibility, and resistance to corrosion, making it the most cost-effective and practical choice for household wiring.

2. Why don’t free electrons in metals create a current without a potential difference?

Without an external potential difference, free electrons undergo rapid, random thermal motion in all directions, causing their net displacement to equal zero.

When a potential difference is applied, an electric field directs these electrons to drift towards the positive terminal, producing a net electric current.

3. How do conventional and actual current directions affect circuit behaviour, and why is conventional current important in diagrams and calculations?

Conventional current flows from positive to negative, while actual electron current flows from negative to positive. However, both yield identical circuit energy transfer and behaviour.

Conventional current remains the universal standard across circuit diagrams, laws such as Kirchhoff’s laws, and mathematical calculations to ensure consistency.

4. Compare EMF and potential difference, and explain why this distinction matters in circuit analysis.

Electromotive force (EMF) is the non-electrical energy converted per unit charge by a source to maintain current, while potential difference (PD) is the electrical energy dissipated per unit charge between two points in a circuit.

Distinguishing them is important because internal battery resistance makes the terminal potential difference lower than the total EMF during discharge.

5. How is a current-carrying wire electrically neutral?

A current-carrying wire remains electrically neutral because the rate at which electrons enter one end equals the rate at which they exit the other end.

The total number of negative electrons continuously equals the total number of positive fixed metal ions, so there is no net charge accumulation inside the conductor.

6. Would the lights still work if a car battery’s positive and negative terminals were interchanged?

Yes, standard incandescent car bulbs would still light up because their resistive heating elements operate independently of current direction.

However, modern vehicle circuits containing polarity-sensitive components such as LEDs, diodes, or electronic control units (ECUs) may fail to function or suffer permanent electrical damage.

7. Evaluate the limits of Ohm’s law for different materials, especially under extreme conditions.

Ohm’s law states:

It applies strictly to ohmic conductors, such as metals, when physical conditions like temperature remain constant.

It fails for non-ohmic devices such as diodes and transistors. It may also become invalid under extreme conditions such as high temperatures, strong electric fields, or cryogenic states where resistivity changes drastically due to thermal effects or superconductivity.

8. How does a wire’s shape affect its resistance? Does bending change it?

Resistance depends on the physical dimensions of a wire:

where:

• \(R\) = resistance

• \(\rho\) = resistivity

• \(L\) = length of the wire

• \(A\) = cross-sectional area

A longer wire has greater resistance, while a larger cross-sectional area decreases resistance.

Smoothly bending a wire does not alter its total length or cross-sectional area, so its electrical resistance remains unchanged.

9. The temperature coefficient of copper is \(0.004\text{ K}^{-1}\). How does this affect copper’s performance in electrical systems under varying temperatures?

A positive temperature coefficient (\(\alpha=0.004\text{ K}^{-1}\)) means copper’s resistance increases as temperature rises.

In high-temperature electrical systems, increased resistance causes greater energy loss as heat:

This reduces operational current efficiency and requires thermal management to prevent overheating.

10. How would you define fluid resistance for a water-carrying pipe?

Fluid resistance is the opposition faced by a flowing fluid due to internal viscous friction and friction against the inner walls of a pipe.

It depends on pipe length, fluid viscosity, and flow conditions. According to Poiseuille’s law, for laminar flow through a cylindrical pipe, fluid resistance is proportional to the inverse fourth power of the pipe radius:

Long Response Questions

1. Explain electric current and its unit (ampere) by exploring charge flow. Discuss the difference between conventional and actual current and when this distinction matters.

Definition and Equation of Electric Current

Electric current (\(I\)) is defined as the net rate of flow of electric charge through any cross-sectional area of a conductor per unit time.

Where:

• \(\Delta Q\) = net charge in coulombs (C).

• \(\Delta t\) = time interval in seconds (s).

Unit of Electric Current (Ampere)

The SI unit of electric current is the ampere (A).

One ampere of current flows through a conductor when one coulomb of charge passes through a given cross-section in one second.

Conventional Current vs. Actual Current

• Conventional Current: This historical convention, established by Benjamin Franklin, assumes current is the flow of positive charges from the positive (higher potential) terminal to the negative (lower potential) terminal.

• Actual (Electron) Current: In metallic conductors, negatively charged free electrons move from the negative terminal towards the positive terminal.

When the Distinction Matters

1. Semiconductor Devices: In p-n junctions, transistors, and electrolytes, both positive charge carriers (holes) and negative charge carriers (electrons or ions) may move simultaneously. Distinguishing carrier-flow directions is important for device modelling.

2. Magnetic Field Forces (Right-Hand Rule): Determining the force direction on moving charges requires knowing the sign of the charge carrier.

3. Electrolysis and Particle Accelerators: Chemical reactions at anodes and cathodes depend directly on the actual direction of ionic drift.

2. Analyse electrical conduction in metals and how external factors like temperature and magnetic fields affect electron movement and conduction efficiency.

Electrical Conduction Mechanism in Metals

Metals consist of a rigid lattice of positive ions surrounded by a cloud of free conduction electrons, as described by the Drude free-electron model.

• In the absence of an electric field, electrons move randomly at high speeds (approximately \(10^6\text{ m/s}\)) due to thermal energy. This results in zero net displacement.

• When an electric field (\(\vec E\)) is applied across the metal, an electrostatic force acts on the electrons:

This establishes a small net drift velocity (\(v_d\approx10^{-4}\text{ m/s}\)) towards the positive terminal.

Effect of External Factors

1. Temperature

• Mechanism: Increasing temperature causes lattice ions to vibrate with larger amplitudes.

• Impact on Efficiency: Conduction electrons collide more frequently with vibrating ions, reducing the mean free path (\(\lambda\)) and relaxation time (\(\tau\)). This increases resistance and reduces conduction efficiency.

2. Magnetic Fields (Hall Effect and Magnetoresistance)

– Mechanism: When a magnetic field (\(\vec B\)) is applied perpendicular to electron flow, electrons experience a magnetic Lorentz force:

– Impact on Efficiency: The Lorentz force deflects electrons towards one side of the conductor, creating a transverse potential difference known as Hall voltage. Magnetoresistance may also change the effective resistance of the conductor.

3. Compare DC and AC in terms of their behaviour in circuit elements. Discuss the pros and cons of each in applications like power transmission and electronics.

Behaviour in Circuit Elements

Capacitive reactance:

Inductive reactance:

Pros and Cons of DC and AC

Direct Current (DC)

Pros:

• Highly stable.

• Essential for digital electronics, microprocessors, battery storage, and electric vehicles.

Cons:

• Difficult to step up or step down voltage efficiently without power electronics.

• Higher transmission losses at low voltages over long distances.

Alternating Current (AC)

Pros:

• Voltage can easily be stepped up or down using transformers.

• High-voltage, low-current transmission reduces \(I^2R\) power losses over long distances.

Cons:

• Cannot be stored directly in batteries.

• Produces electromagnetic interference (EMI).

• Skin effect increases effective wire resistance at high frequencies.

4. Examine electromotive force (EMF) and its role in maintaining current.

Definition and Concept of EMF

Electromotive force (\(\mathcal{E}\)) is the maximum potential difference supplied by a source, such as a battery, generator, or solar cell, when no current is being drawn from it.

Mathematically, it is the work done (\(W\)) per unit charge (\(q\)) by non-electrical forces inside the source:

Role of EMF in Maintaining Current

1. Energy Supply: In a closed circuit, electric current flows through resistors, converting electrical energy into heat, light, or mechanical work. Without a source, the potential differences dissipate rapidly.

2. Pumping Action: The EMF source acts as a chemical or mechanical pump that pushes positive charges from low potential (negative terminal) to high potential (positive terminal) inside the battery against the internal electric field.

3. Maintaining Steady State: By continuously restoring electrostatic potential energy to passing charges, the EMF source maintains a steady potential difference across the external circuit, driving continuous current flow.

5. Distinguish between EMF and potential difference, using real-world examples like batteries.

Comparison Between EMF and Potential Difference

Real-World Example: Automobile Battery

Consider a standard 12.0 V car battery with an internal resistance of \(r=0.05\,\Omega\).

Open Circuit Condition

When no load is connected (\(I=0\)), a voltmeter across the battery terminals reads its full EMF:

Closed Circuit Condition (Engine Start)

When starting the engine, a large current of \(I=100\text{ A}\) is drawn.

The internal voltage drop is:

The measured terminal potential difference becomes:

6. Critically analyse Ohm’s law and its limitations for non-ohmic devices. Discuss the importance of I-V graphs and propose experiments to explore non-linear materials.

Critical Analysis of Ohm’s Law

Ohm’s law states that the current (\(I\)) flowing through a conductor is directly proportional to the potential difference (\(V\)) applied across it, provided physical conditions such as temperature remain constant.

Ohm’s law is an empirical relationship valid for specific materials and conditions, such as metals at moderate temperatures.

Limitations and Non-Ohmic Devices

• Filament Bulb: As current increases, thermal heating increases resistance, making the I-V graph nonlinear.

• Semiconductor Diode: Allows current mainly in one direction after reaching a knee voltage (approximately 0.7 V for silicon). Its behaviour is nonlinear.

• Thermistor: Its resistance decreases as temperature increases when it has a negative temperature coefficient.

Importance of I-V Graphs

I-V characteristic curves provide a visual representation of a component’s behaviour.

The dynamic resistance at any point is given by:

Proposed Experiment to Explore Non-Linear Materials (Semiconductor Diode)

Apparatus:

• Variable DC power supply.

• Ammeter (mA).

• Voltmeter.

• \(1\,k\Omega\) resistor (current limiter).

• Semiconductor diode (1N4007).

Procedure:

1. Connect the diode in series with the resistor and ammeter across the power supply.

2. Connect the voltmeter in parallel across the diode.

3. Increase the supply voltage in steps of 0.1 V and record the diode terminal voltage (\(V_D\)) and current (\(I_D\)).

Analysis:

Plot \(I_D\) on the y-axis against \(V_D\) on the x-axis. The resulting exponential nonlinear curve illustrates the non-ohmic behaviour of the diode.

7. Investigate the relationship between resistance and resistivity and design an experiment to measure resistance. Discuss factors affecting accuracy, such as temperature.

Relationship Between Resistance and Resistivity

Resistance (\(R\)) is an extrinsic property dependent on the dimensions of a conductor, whereas resistivity (\(\rho\)) is an intrinsic property dependent on material composition and temperature.

They are related by:

Where:

• \(L\) = length of conductor (m).

• \(A\) = cross-sectional area (m\(^2\)).

Experimental Design to Measure Resistance (Voltmeter-Ammeter Method)

Setup:

Connect a test wire of length \(L\) in series with a DC power supply, a rheostat, and a digital ammeter. Connect a digital voltmeter in parallel across the test wire.

Measurement:

Vary the rheostat to record five sets of voltage (\(V\)) and current (\(I\)) readings.

Calculation:

Calculate resistance for each trial:

Take the average or determine the resistance from the slope of the V-I graph.

Factors Affecting Accuracy

1. Temperature Fluctuations: Current flow causes Joule heating (\(I^2R\)), increasing resistivity.

Mitigation: Use low currents and take readings quickly.

2. Contact Resistance: Resistance at terminal connection points can add systematic error.

Mitigation: Use four-wire sensing (Kelvin connection).

3. Meter Resistance: A voltmeter draws a small current, while an ammeter produces an internal voltage drop. These effects can influence measurements.

8. Analyse how factors like temperature, material, length, and area affect resistance. Discuss practical applications, such as wiring or heating elements, and ways to optimize resistance.

Factors Affecting Resistance

1. Length (\(L\))

Longer paths present more collisions for electrons and increase resistance.

2. Cross-Sectional Area (\(A\))

Wider cross-sections provide more paths for electrons and decrease resistance.

3. Material (\(\rho\))

Resistivity depends on the material’s properties and the availability of free charge carriers. Metals generally have low resistivity, while insulators have high resistivity.

4. Temperature (\(T\))

In metals, increasing temperature increases lattice vibrations, leading to greater resistance.

Practical Applications

– Household Wiring: Requires minimal energy loss. Thick copper or aluminium wires are used to provide a large cross-sectional area and low resistance.

– Heating Elements (Nichrome): Require high heat generation. Nichrome has high resistivity and is commonly formed into long, thin coils.

Optimization Strategies

• Minimize unwanted circuit resistance by selecting materials with high conductivity, such as copper and silver, and increasing wire diameter.

• Maximize heat production in appliances by selecting high-resistivity alloys such as Nichrome, designed to withstand high operating temperatures without oxidizing.

9. How does temperature influence the resistance of materials, and what implications does this have for electrical components in different environments?

Temperature Influence by Material Class

1. Metals (Conductors)

Metals have a positive temperature coefficient (\(\alpha>0\)). Higher temperatures increase thermal lattice vibrations, causing more electron collisions and increased resistance.

2. Semiconductors (Silicon and Germanium)

Semiconductors generally have a negative temperature coefficient (\(\alpha<0\)). Thermal energy breaks covalent bonds, releasing more electron-hole charge carriers, which significantly decreases resistance.

3. Superconductors

Below a critical temperature (\(T_c\)), the electrical resistance of a superconductor drops abruptly to zero:

Environmental and Practical Implications

• High-Temperature Environments: Industrial machinery and transformers experience higher internal resistance, leading to greater energy losses and potential overheating.

• Cryogenic and Computing Environments: Superconducting magnets used in MRI systems require cooling to cryogenic temperatures. This allows them to operate with zero electrical resistance below their critical temperature.

10. Examine the placement of ammeters and voltmeters in circuits and how misconnection affects measurement. Propose strategies to avoid errors.

Correct Placement and Ideal Characteristics

Consequences of Misconnection

1. Voltmeter Connected in Series

• Its high internal resistance (\(r_V\approx M\Omega\)) reduces the total circuit current to nearly zero (\(I\approx0\)).

• The circuit may stop functioning, and the voltmeter may simply read the supply EMF.

2. Ammeter Connected in Parallel

• Its extremely low internal resistance (\(r_A\approx0\)) creates a direct short circuit across the component.

• A massive surge of current flows through the ammeter, which can blow its internal fuse or permanently damage the instrument.

Strategies to Avoid Errors

• Double-check circuit connections before switching on the power: ammeters in series and voltmeters in parallel.

• Select digital meters with high input impedance (greater than \(10\,M\Omega\)) for voltage measurements.

• Always begin measurements using the highest current or voltage scale to prevent overload.

Numerical Response Questions

1. How much time will it take to charge a 200 Ah battery when it is connected to a current of 25 A?

Given:

Battery capacity:

Charging current:

Formula:

Rearranging:

Calculation:

Answer:

2. A 12.0 V EMF source is connected to a purely resistive electrical appliance (a light bulb). An electric current of 2.0 A flows through it. Consider the conducting wires to be resistance-free. Calculate the resistance offered by the electrical appliance.

Given:

Voltage:

Current:

Formula (Ohm’s Law):

Rearranging:

Calculation:

Answer:

3. The potential difference across the two ends of a component decreases to one fourth of its initial value while its resistance remains constant. What change will occur in the current through it?

Given:

Initial potential difference:

Final potential difference:

Resistance:

Formula:

Calculation:

Initial current:

Final current:

Substituting:

Answer:

The current decreases to one fourth of its initial value.

4. What voltage is necessary to pass a current of 50 amperes through a resistance of 100 \(\Omega\)?

Given:

Current:

Resistance:

Formula:

Calculation:

Answer:

5. The current passing through a resistor in a circuit is 0.5 A when the voltage across it is 6.0 V. What current will pass through the same resistor when the voltage across it is 9.0 V?

Given:

Initial voltage:

Initial current:

New voltage:

Step 1: Find Resistance (\(R\))

Using Ohm’s law:

Step 2: Find New Current (\(I_2\))

Answer:

6. The length and area of a wire are given as 2 m and 0.4 mm\(^2\), respectively. The resistance of that wire is 0.085 \(\Omega\). Calculate the resistivity.

Given:

Length:

Area:

Converting area into square metres:

Resistance:

Formula:

Rearranging:

Calculation:

Answer:

7. Resistivity of a given copper wire of length 2 m is \(1.7\times10^{-8}\,\Omega\cdot\text{m}\).

(a) If the wire is stretched to double its length, what will be the new resistivity?

Concept:

Resistivity (\(\rho\)) is an intrinsic property of a material. It depends on the material and temperature, not on its dimensions such as length or area.

Therefore, doubling the length of the wire does not change its resistivity, provided its material and temperature remain unchanged.

Answer (a):

(b) If its temperature is increased by 20 K, find the new resistivity. Take \(\alpha=3.9\times10^{-3}\text{ K}^{-1}\).

Given:

Initial resistivity:

Temperature change:

Temperature coefficient:

Formula:

Calculation:

Answer (b):

8. At some temperature \(T_0\), the resistivity of a metallic conductor is \(1.7\times10^{-8}\,\Omega\cdot\text{m}\). If the temperature is increased by 50 K, find the new resistivity by taking the temperature coefficient of resistivity as 0.004.

Given:

Initial resistivity:

Temperature change:

Temperature coefficient:

Formula:

Calculation:

Answer:

Notes by Sir Dilawar

For more notes, visit QuranEducationPoint.com