Problem 8: Consider the following figure. r = 2.0 Ω E = 18 V r = 1.0 Ω E = 12 V R = 4.8 Ω a) Calculate the current flowing in the circuit. b) Determine the terminal voltage of each battery in the figure.

(a) Determine the equilibrium charge on the capacitor in the circuit of Figure P27.46 as a function of R. (b) Evaluate the charge when R = 10.0 . (c) Can the charge on the capacitor be zero? If so, for what value of R? (d) What is the maximum possible magnitude of the charge on the capacitor? For what value of R is it achieved? (c) Is it experimentally meaningful to take R = ? Explain your answer. If so, what charge magnitude does it imply? Figure P27.46

Consider the circuit shown below where four capacitors, C1=2.7 µF, C2=3.8 µF , C3=3.6 µF and C4=2.1 µF are connected to a battery of voltage V=47 V. Determine the voltage on C4. Express your answer using one decimal place in units of Volts. C2 C1 C3 C4 V

Four capacitors are arranged in the circuit shown in the figure. The capacitors have the values C 3 26.5 иF, С2 — 45.5 pF, C3 = 50.5 µF, and C4 40.5 µF, and the power supply is at %3D voltage V = 19.5 V. C, What is the equivalent capacitance of the circuit? V equivalent capacitance: 14.14 µF What is the charge on capacitor C2? 4.03 x10-4 charge on C2: C Incorrect What is the potential difference across capacitor C3? potential difference across C3: V Incorrect What is the potential energy stored in capacitor C4 ? potential energy stored in C4: J Incorrect

b. The voltage across the plates of a capacitor at any time t seconds is given by t V(t) = Ve¯RC where V, C and R are constants. Given V = 200 volts, C = 0.1 x 10-6 Farads and R = 4 x 105 ohms. Find i. The initial rate of change of voltage ii. The rate of change of voltage after 0.5 s.

The initial voltage across the capacitor at t = 0 in the circuit shown in Figure is 8 V. 4 kn 3 1 kn 2 kn R5 1 kl Vo =8V 2 kl a. Write a node equation at node 1 by summing the currents away from node 1. Notice that the voltage at node 3 is given by v3(t) = v(t). b. Write a node equation at node 2 by summing the currents away from node 2. Notice that the voltage at node 3 is given by v3(!) = v(t). c. Solve the two node equations from (a) and (b) to express v,(t) as a function of v(t), and va(t) as a function of v(t). d. Write a node equation at node 3 by summing the currents away from node 3. Use the results from (c) to simplify the equation as a first- order differential equation of v(t). e. Solve the differential equation to find the voltage v(t), t 2 0, across the capacitor and plot v(t).

24.0 V 4.00 A R 4.00 A Figure N 8. Consider the circuit shown in Figure b. The terminal voltage of the 24.0 V battery is 21.2 V. What is a) the internal resistance r of the battery; b) the resistance R of the circuit resistor???

Four capacitors are arranged in the circuit shown in the figure. The capacitors have the values C, = 25.5 µF, C = 45.5 µF, C3 = 50.5 µF, and C4 = 40.5 µF, and the power supply is at voltage V = 32.5 V. What is the equivalent capacitance of the circuit? equivalent capacitance: 13.24 What is the charge on capacitor C2 ? charge on C: 297.9 x10-6 What is the potential difference across capacitor C3? ас potential difference across C3: 3.28 V

Consider the circuit shown in (Figure 1). Assume E = 15 V. a)What is the charge on 3.0 μFcapacitor? Express your answer with the appropriate units. b)What is the charge on 4.0 μF capacitor? Express your answer with the appropriate units. c)What is the charge on 6.0 μF capacitor? Express your answer with the appropriate units.

Two capacitors of Q1 = 5.0 μF and Q2 = 6.0 μF are connected in parallel. These capacitors are connected in series with a Q3 = 7.0 μF capacitor across a 220 V. A) Draw a circuit for this configuration. B) Find the charge stored in each capacitor