1. Consider the circuit shown.

(a) Calculate the equivalent capacitance of the capacitor bank.

(b) What is the potential difference across the plates of the 2.00 µF capacitor?

(b) How much energy is stored in the charged capacitor bank?

2. The parallel plates of an air-filled capacitor are 1.10 mm apart.

(a) What must be the area of this device if the capacitance is to be 0.225 µF?

The capacitor is to be charged to a potential difference of 25.0 V, then isolated and the region between the plates filled completely with transformer oil (k = 4.50).

(b) What is the value of the capacitance after this is done?

(c) What will be the potential difference after this is done?

3. A potential difference of 25.0 V is maintained between the ends of an aluminum wire 65.0 m long. The resistance of this wire is 0.210 ohms. The resistivity of Al is 2.75 x 10^-8 ohm·m.

(a) Calculate the cross-sectional area of this wire.

(b) Calculate the magnitude of the electric field in this wire.

(c) Calculate the current through this wire.

(d) Calculate the rate that electrical energy is being converted to heat in this wire.

4. A 2.00 µF capacitor is charged to a potential difference of 15.5 V. This capacitor is then discharged through a 3.50 x 10⁶ ohm resistor.

(a) Calculate the time constant of this circuit.

(b) How much charge was initially (before discharge started) on the capacitor?

(c) What is the potential difference between the plates of the capacitor 7.00 s after the resistor is connected?

5. Consider the circuit shown.

(a) Determine the equivalent resistance of the circuit.

(b) What is the potential difference across the 2.0 ohm resistor?

(c) At what rate is the battery supplying energy to the circuit?

6. A charged particle is accelerated from rest through an electric potential difference of 1.75 x 10⁴ V and then enters a uniform magnetic field of 2.50 T perpendicular to the path. (q = 1.60 x 10^-19 C, m = 1.67 x 10^-27 kg)

(a) Calculate the speed of the particle as it enters the magnetic field.

(b) Calculate the radius of the circular path followed by the particle while it is in the magnetic field.

(c) What is the angular speed of the particle in the magnetic field?

7. A 25.0 cm long straight segment of wire, carrying a current of 155 A directly west, is situated in a magnetic field of 5.00 x 10^-5 T. This field is directed north and downward at an angle of 50.0^o with the horizontal as shown.

Calculate the magnitude of the magnetic force on the segment of wire.

1  a. 4.00 µF   b. 12.0 V   c. 2.88 x 10^-4 J

2  a. 28.0 m²   b. 1.01 µF   c. 5.56 V

3  a. 8.51 x 10^-6 m²   b. 0.385 V/m   c. 119 A   d. 2.98 kW

4  a. 7.00 s   b. 3.10 x 10^-5 C   c. 5.70 V

5  a. 2.7 ohm   b. 11.3 V   c. 120 W

6  a. 1.83 x 10⁶ m/s   b. 7.65 mm   c. 2.40 x 10⁸ rad/s

7.  1.94 x 10^-3 N