PHYS 102 Quiz Problems Chapter 27 : Circuits Dr. M. F. Al-Kuhaili 1. (TERM 002) (a) Calculate the current through each resistor, assuming that the batteries are ideal. (b) Calculate the potential difference V a V b. Take R 1 = 5.0 Ω, R 2 = 10 Ω, E 1 = 6.0 V and E 2 = E 3 = 9.0 V. 2. (TERM 002) A 2.0 MΩ resistor and a 2.00 µf capacitor are connected in series and then a 15.0 V potential difference is suddenly applied across them. Assume that the battery is connected at t = 0. (a) At what rate is the charge of the capacitor increasing at t = 2.0 s? (b) At what rate is the energy being stored in the capacitor at t = 2.0 s? (c) At what rate is thermal energy appearing in the resistor at t = 2.0 s? (d) At what rate is energy being delivered by the battery at t = 2.0 s? 3. (TERM 002) A circuit containing five resistors connected to a battery with a 12.0 V emf is shown in the figure. What is the potential difference across the 5.0 Ω resistor? 4. (TERM 002) In the figure, E 1 = 6.00 V, E 2 = 3.00 V, R 1 = 10.0 Ω, R 2 = 15.0 Ω, R 3 = 20.0 Ω, and both batteries are ideal. What is power dissipated in each resistor? 5. (TERM 012) In the circuit shown, E 1 = 6.00 V, E 2 = 12.0 V, R 1 = 200 Ω and R 2 = 100 Ω. What is the magnitude and direction of the current through resistor R 2?
6. (TERM 012) In the circuit shown, find the current in each resistor. 7. (TERM 021) In the circuit shown, if V d V c = - 5.0 V, what is the emf of the battery? 8. (TERM 021) Calculate the emf of the battery shown in the circuit. 9. (TERM 022) In the circuit shown, R = 3.0 Ω and E = 10 V. What is the power dissipated in R? 10. (TERM 022) In the circuit shown, the two resistors are identical and each has a value of 5.0 Ω, and E has a value of 5.0 V. What is the current supplied by the resistor? 11. (TERM 022) In the circuit shown, what is the power dissipated in each of the 4.0-Ω resistors?
12. (TERM 033) In the figure below: R 1 = 10 Ω, R 2 = 20 Ω, E = 12 V and I = 0.5 A. What is the value of R 3? 13. (TERM 042) In the circuit shown below, the power dissipated in R 1 is 20.0 W. (a) Find R 1. (b) What is the emf of the battery? (c) Find the current through the 10.0-Ω resistor. (d) Find the current through R 2. 14. (TERM 042) In the circuit shown below: (a) What are the magnitude and direction of the current through the resistor R? (b) What is the value of R? (c) What is the value of the unknown emf E? 15. (TERM 042) In the circuit shown below: (a) What is the equivalent resistance of the four resistors shown? (b) What is the current through the battery? (c) What is the current through each resistor? 16. (TERM 052) In the circuit shown below, R 1 = 8 Ω, R 2 = 6 Ω, R 3 = 6 Ω, and R 4 = 10 Ω. The current i = 1.7 A. (a) What is the emf of the ideal battery? (b) What is the magnitude of the current in resistor R 2? 17. (TERM 052) In an RC series circuit, E = 12.0 V, R = 1.50 MΩ, and C = 1.75 µf. (a) Calculate the time constant? (b) Find the maximum charge that will appear on the capacitor? (c) How long does it take for the charge on the capacitor to be 16.0 µc?
18. (TERM 052) In the circuit shown below, R 1 = 100 Ω, R 2 = 80 Ω, and the ideal batteries have emfs E 1 = 6 V, E 2 = 5 V, and E 3 = 8 V. (a) What is the magnitude of the current in resistor R 1? (b) What is the magnitude of the current in resistor R 2? (c) What is the potential difference V b V a? 19. (TERM 061) In the circuit shown, a 12.0-V battery is used to charge the capacitor. The switch S is closed at t = 0. Take C = 25.0 µf and R = 15.0 kω. a) What is the time constant τ of the RC circuit? b) What is the charge on the capacitor at t = 0.75 s? c) What is the potential difference across the capacitor at t = 0.75 s? 20. (TERM 061) Consider the circuit shown below. A potential difference of 25 V is applied between points a and b. a) Find the equivalent resistance between points a and b? b) What is the current in the 4 Ω resistor? c) What is the current in the 10 Ω resistor? 21. (TERM 061) Two identical batteries of emf E = 1.5 V and internal resistance r = 0.2 Ω are connected as shown in the figure below to an external resistor R = 5.0 Ω. a) What is the current in resistance R? b) What is the rate P at which energy is dissipated in R?
22. (TERM 062) In an RC circuit, an ideal battery with emf E = 12.0 V is connected in series to a resistor of resistance R = 1.40 MΩ and a capacitor of capacitance C = 1.80 µf. a) Calculate the time constant. b) Find the maximum charge that will appear on the capacitor. c) How long does it take for the charge to build up to 1.6 µc? 23. (TERM 062) In the circuit shown below, the battery is ideal with emf E = 5.0 V. The values of the resistances are: R 1 = 100 Ω, R 2 = 50 Ω, R 3 = 50 Ω, and R 4 = 75 Ω. a) What is the equivalent resistance of the resistor? b) What is the current supplied by the battery? c) What is the power supplied by the battery? 24. (TERM 062) In the circuit shown below, the batteries are ideal with emfs E 1 = 6.0 V, E 2 = 5.0 V, and E 3 = 4.0 V. The values of the resistances are: R 1 = 100 Ω, and R 2 = 50 Ω. a) Calculate the current in each resistor. b) What is the potential difference V a V b? 25. (TERM 063) In the circuit shown below: R 1 = 6.0 Ω, R 2 = 12 Ω, R 3 = 4.0 Ω, R 4 = 3.0 Ω, and R 5 = 5.0 Ω. (a) What is the equivalent resistance? (b) What is the magnitude of the current in R 5? 26. (TERM 063) In figure below, all the resistors have a value of 5 Ω. The battery is ideal with an emf = 20 V. (a) What is the equivalent resistance? (b) What is the value of the current passing through R 3?
27. (TERM 063) Determine the power dissipated by the 40-Ω resistor in the circuit shown. 28. (TERM 071) In the circuit shown below, I 1 = 0.15 A and I 2 = 2.22 A. (a) What is the value of I 3? (b) What is the value of the emf (ε) of the battery on the right? (c) What is the value of the potential difference V a V b? 29. (TERM 071) In the circuit shown below, I = 0.65 A and R = 5Ω. What is the value of the emf ε? 30. (TERM 071) In the circuit shown below, the emf of the battery is ε = 10 V, and the value of each resistance is R = 30 Ω. (a) What is the equivalent resistance of the circuit? (b) What is the value of the current I?