⚡ Electricity & Circuits — Practice Worksheet

Q1. The equivalent resistance of two resistors 6 Ω and 3 Ω connected in parallel is:

1. 9 Ω
2. 2 Ω
3. 4.5 Ω
4. 1 Ω

Q2. In a Wheatstone bridge, if P = 100 Ω, Q = 200 Ω, R = 40 Ω, the value of S for balance is:

1. 20 Ω
2. 40 Ω
3. 80 Ω
4. 160 Ω

Q3. The drift velocity of electrons in a conductor carrying current I with cross-sectional area A and electron density n is:

1. I / (nAe)
2. nAe / I
3. I × nAe
4. I / (ne)

Q4. A cell of EMF 2 V and internal resistance 1 Ω is connected to an external resistance of 4 Ω. The current in the circuit is:

1. 0.4 A
2. 0.5 A
3. 2 A
4. 0.8 A

Q5. Kirchhoff's junction rule is based on conservation of:

1. Energy
2. Charge
3. Momentum
4. Mass

Q6. The resistivity of a conductor depends on:

1. Length of the conductor
2. Area of cross-section
3. Material and temperature
4. Applied voltage

Q7. Five identical resistors each of resistance R are connected as shown in a balanced Wheatstone bridge with one resistor across the galvanometer arm. The equivalent resistance between the two ends is:

1. R
2. 2R
3. R/2
4. 5R

Q8. The power dissipated in a resistor R connected across a battery of EMF ε and internal resistance r is maximum when:

1. R = 0
2. R = r
3. R = 2r
4. R → ∞

Q9. A potentiometer wire of length 100 cm has a resistance of 10 Ω. It is connected in series with a resistance of 40 Ω and a battery of EMF 2 V. The potential gradient along the wire is:

1. 0.02 V/cm
2. 0.004 V/cm
3. 0.04 V/cm
4. 0.2 V/cm

Q10. The temperature coefficient of resistance is positive for:

1. Semiconductors
2. Insulators
3. Metals
4. Superconductors

Q11. Two cells of EMF 1.5 V and 2 V with internal resistances 1 Ω and 2 Ω respectively are connected in parallel. The equivalent EMF is:

1. 1.67 V
2. 1.75 V
3. 3.5 V
4. 2.0 V

Q12. In a meter bridge experiment, the balance point is obtained at 40 cm from the left end. If the known resistance is 6 Ω, the unknown resistance is:

1. 4 Ω
2. 9 Ω
3. 6 Ω
4. 2.4 Ω

Q13. A wire of resistance 12 Ω is bent into a circle. The effective resistance between two diametrically opposite points is:

1. 12 Ω
2. 6 Ω
3. 3 Ω
4. 24 Ω

Q14. An electric heater rated 1000 W, 220 V is connected to a 110 V supply. The power consumed is:

1. 1000 W
2. 500 W
3. 250 W
4. 750 W

Q15. The colour code of a resistor is Brown-Black-Red-Gold. Its resistance is:

1. 100 Ω ± 5%
2. 1000 Ω ± 5%
3. 10 Ω ± 5%
4. 10000 Ω ± 5%

Q16. A galvanometer of resistance 50 Ω gives full-scale deflection for 1 mA. The shunt resistance to convert it into an ammeter of range 1 A is approximately:

1. 0.05 Ω
2. 0.5 Ω
3. 5 Ω
4. 50 Ω

Q17. In a series LCR circuit at resonance, the impedance is:

1. Maximum
2. Minimum and equal to R
3. Zero
4. Equal to √(L/C)

Q18. The time constant of an RC circuit with R = 1 MΩ and C = 1 μF is:

1. 1 s
2. 1 ms
3. 1 μs
4. 10 s

Q19. A copper wire of length 2 m and cross-sectional area 1 mm² has resistivity 1.7 × 10⁻⁸ Ω·m. Find its resistance.

Q20. Three resistors of 2 Ω, 3 Ω, and 6 Ω are connected in parallel. This combination is connected in series with a 1 Ω resistor and a 6 V battery. Find the current through each resistor.

Q21. A battery of EMF 12 V and internal resistance 2 Ω is connected to two resistors of 4 Ω each in parallel. Find the terminal voltage and power delivered to the external circuit.

Q22. Using Kirchhoff's laws, find the current through each branch of a circuit with two loops: Loop 1 has a 10 V battery and resistors 5 Ω and 10 Ω; Loop 2 has a 5 V battery and resistors 10 Ω and 15 Ω. The 10 Ω resistor is common to both loops.

Q23. A potentiometer wire of length 1 m balances a cell of EMF 1.02 V at 51 cm. Find the EMF of another cell that balances at 75 cm.

Q24. An electric kettle rated 2000 W is used to heat 1 kg of water from 20°C to 100°C. Find the time taken (specific heat of water = 4200 J/kg·K). Assume no heat loss.

Q25. A 12 V battery charges a 100 μF capacitor through a 10 kΩ resistor. Find the time constant, and the charge and voltage across the capacitor after one time constant.

Q26. A wire of resistance R is stretched to double its length. Find the new resistance in terms of R.

Q27. In a meter bridge, the null point is at 33.3 cm with a 10 Ω resistance in the right gap. Find the unknown resistance. If the wire has a total resistance of 1 Ω, find the percentage error introduced.

Q28. A galvanometer with resistance 100 Ω and full-scale deflection current 50 μA is to be converted into a voltmeter of range 0–10 V. Find the required series resistance.

Q29. Five cells each of EMF 1.5 V and internal resistance 0.5 Ω are connected in series with an external resistance of 7.5 Ω. Find the current and power dissipated in the external resistance.

Q30. A network consists of 12 identical resistors each of resistance R forming the edges of a cube. Find the equivalent resistance between two diagonally opposite corners of the cube.