(a)
The charge on the capacitor
(a)
Answer to Problem 69P
The charge on the capacitor
Explanation of Solution
The switch is closed in the electric circuit and the current exists in a simple series circuit as shown in figure
Write the expression for the power delivered to the resistor.
Here,
Use equation (I) to solve for
Write the expression for the potential difference across the resistor
Here,
Write the expression for the charge on the capacitor
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the charge on the capacitor
(b)
The amount of charge on the capacitor
(b)
Answer to Problem 69P
The amount of charge on the capacitor
Explanation of Solution
Consider the switch is closed to find the emf of the battery and the charge in the capacitor
Write the expression for the potential difference across
Write the expression for the charge on the capacitor
Write the expression for the emf of the battery.
Here,
Write the expression for
Use equation (VIII) in (VII) to solve for
Here,
After the switch is opened, no current exists. The potential difference across each resistor is zero. The emf of the battery appears across both capacitors.
Write the expression for the new charge on the
Write the expression for the amount of the charge on the capacitor is changed
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the amount of charge on the capacitor
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Chapter 21 Solutions
Principles of Physics
- In the circuit of Figure P21.57, the switch S has been open for a long time. It is then suddenly closed. Take = 10.0 V, R1 = 50.0 k, R2 = 100 k, and C = 10.0 F. Determine the time constant (a) before the switch is closed and (b) after the switch is closed. (c) Let the switch be closed at t = 0. Determine the current in the switch as a function of time.arrow_forwardA battery with = 6.00 V and no internal resistance supplies current to the circuit shown in Figure P27.9. When the double-throw switch S is open as shown in the figure, the current in the battery is 1.00 mA. When the switch is closed in position a, the current in the battery is 1.20 mA. When the switch is closed in position b, the current in the battery is 2.00 mA. Find the resistances (a) R1, (b) R2, and (c) R3. Figure P27.9 Problems 9 and 10.arrow_forwardAn electric eel generates electric currents through its highly specialized Hunters organ, in which thousands of disk-shaped cells called electrocytes are lined up in series, very much in the same way batteries are lined up inside a flashlight. When activated, each electrocyte can maintain a potential difference of about 150 mV at a current of 1.0 A for about 2.0 ms. Suppose a grown electric eel has 4.0 103 electrocytes and can deliver up to 3.00 102 shocks in rapid series over about 1.0 s. (a) What maximum electrical power can an electric eel generate? (b) Approximately how much energy does it release in one shock? (c) How high would a mass of 1.0 kg have to be lifted so that its gravitational potential energy equals the energy released in 3.00 102 such shocks?arrow_forward
- Integrated Concepts (a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of 1.00102 MV, and a length of 1.00 ms? (b) What mass of tree sap could be raised from 18.0°C to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?arrow_forwardA potential difference of 1.00 V is maintained across a 10.0- resistor for a period of 20.0 s. What total charge passes by a point in one of the wires connected to the resistor in this time interval? (a) 200 C (b) 20.0 C (c) 2.00 C (d) 0.005 00 C (e) 0.050 0 Carrow_forwardFigure P18.37 shows a simplified model of a cardiac defibrillator, a device used to patients in ventricular fibrillation. When the switch S is toggled to the left, the capacitor C charges through the resistor R .When the switch is toggled to the right, the capacitor discharges current through the patients torso, modeled as the resistor Rtorso, allowing the hearts normal rhythm to be reestablished. (a) If the capacitor is initially uncharged with C = 8.00 F and = 1250 V, find the value of R required to charge the capacitor to a voltage of 775 V in 1.50 s. (b) If the capacitor is then discharged across the patients torso with, Rtorso = 1250 , calculate the voltage across the capacitor after 5.00 ms. Figure P18.37arrow_forward
- When the switch is open in Figure 18.8, power Po is delivered to the resistor R1. When the switch is closed, which of the following is true about the power Pc delivered to R1? (Neglect the internal resistance of the battery.) (a) Pc Po (b) Pc = Po (c) Pc Po Figure 18.8 (Quick Quizzes 18.5 and 18.6)arrow_forwardThe values of the components in a simple series RC circuit containing a switch (Fig. P21.53) are C = 1.00 F, R = 2.00 106 , and = 10.0 V. At the instant 10.0 s after the switch is closed, calculate (a) the charge on the capacitor, (b) the current in the resistor, (c) the rate at which energy is being stored in the capacitor, and (d) the rate at which energy is being delivered by the battery.arrow_forwardIn the circuit of Figure P27.25, the switch S has been open for a long time. It is then suddenly closed. Take = 10.0 V, R1 = 50.0 k, R2 = 100 k, and C = 10.0 F. Determine the time constant (a) before the switch is closed and (b) after the switch is closed. (c) Let the switch be closed at t = 0. Determine the current in the switch as a function of time. Figure P27.25 Problems 25 and 26.arrow_forward
- When the switch is open in Figure 18.8, power Po is delivered to the resistor R1. When the switch is closed, which of the following is true about the power Pc delivered to R1? (Neglect the internal resistance of the battery.) (a) Pc Po (b) Pc = Po (c) Pc Po Figure 18.8 (Quick Quizzes 18.5 and 18.6)arrow_forwardWhen operating on a 120-V circuit, an electric heater receives 1.30 103 W of power, a toaster receives 1.00 103 W, and an electric oven receives 1.54 103 W. If all three appliances are connected in parallel on a 120-V circuit and turned on, what is the total current drawn from an external source? (a) 24.0 A (b) 32.0 A (c) 40.0 A (d) 48.0 A (e) none of those answersarrow_forwardFigure P18.37 shows a simplified model of a cardiac defibrillator, a device used to patients in ventricular fibrillation. When the switch S is toggled to the left, the capacitor C charges through the resistor R .When the switch is toggled to the right, the capacitor discharges current through the patients torso, modeled as the resistor Rtorso, allowing the hearts normal rhythm to be reestablished. (a) If the capacitor is initially uncharged with C = 8.00 F and = 1250 V, find the value of R required to charge the capacitor to a voltage of 775 V in 1.50 s. (b) If the capacitor is then discharged across the patients torso with, Rtorso = 1250 , calculate the voltage across the capacitor after 5.00 ms. Figure P18.37arrow_forward
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