Question 1

RC circuits: For the circuit shown in the figure, the capacitors are all initially uncharged, the connecting leads have no resistance, the battery has no appreciable internal resistance, and the switch S is originally open.  (a) Just after closing the switch S, what is the current in the 15.0-Ω resistor? 
A) 0.00 A
B) 1.67 A
C) 2.50 A
D) 3.33 A
E) 5.00 A
(b) After the switch S has been closed for a very long time, what is the potential difference across the 28.0-μF capacitor?
A) 0.00 V
B) 25.0 V
C) 3.33 V
D) 37.5 V
E) 50.0 V

Accepted Answer

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Question 2

Meters: A galvanometer has an internal resistance of 100 Ω and deflects full-scale at 2.00 mA. What size resistor should be added to the galvanometer to convert it to a milliammeter capable of reading up to 4.00 mA, and how should this resistor be connected to the galvanometer?

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Question 3

RC circuits: An uncharged 30.0-µF capacitor is connected in series with a 25.0-Ω resistor, a DC battery, and an open switch. The battery has an internal resistance of 10.0 Ω and the open-circuit voltage across its terminals is 50.0 V. The leads have no appreciable resistance. At time t = 0, the switch is suddenly closed.
(a) What is the maximum current through the 25.0-Ω resistor and when does it occur (immediately after closing the switch or after the switch has been closed for a long time)?
(b) What is the maximum charge that the capacitor receives?
(c) When the current in the circuit is 0.850 A, how much charge is on the plates of the capacitor?

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Question 4

RC circuits: For the circuit shown in the figure, the switch S is initially open and the capacitor voltage is 80 V. The switch is then closed at time t = 0. How long after closing the switch will the current in the resistor be 7.0 µA?

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Question 5

Meters: In the circuit shown in the figure, two 360.0-Ω resistors are connected in series with an ideal source of emf. A voltmeter with internal resistance of 6350 Ω is connected across one of the resistors and reads 3.23 V. Find the emf of the source.

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Question 6

RC circuits: A 4.0-μF capacitor that is initially uncharged is connected in series with a 4.0-kΩ resistor and an ideal 17.0-V battery. How much energy is stored in the capacitor 17 ms after the battery has been connected?

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Question 7

Meters: A galvanometer with a resistance of 40.0 Ω deflects full scale at a current of 2.0 mA. What resistance should be used with this galvanometer in order to construct a voltmeter that can read a maximum of 50 V?

Accepted Answer

To convert the galvanometer to a voltmeter that reads up to 50 V, use the formula R = (V/I) - Rg, where V is the maximum voltage (50 V), I is the full-scale deflection current (2.0 mA), and Rg is the galvanometer resistance (40 Ω). R = (50/0.002) - 40 = 25000 - 40 = 24960 Ω, which is approximately 25 kΩ.

Question 8

RC circuits: For the circuit shown in the figure, the switch S is initially open and the capacitor is uncharged. The switch is then closed at time t = 0. How many seconds after closing the switch will the energy stored in the capacitor be equal to 50.2 mJ?

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Question 9

RC circuits: A 6.0-μF capacitor is connected in series with a 5.0 MΩ resistor, and this combination is connected across an ideal 15-V DC battery. What is the current in the circuit when the capacitor has reached 20% of its maximum charge?

Accepted Answer

When the capacitor has reached 20% of its maximum charge, we know that the voltage across the capacitor is 0.2 times the total voltage of the battery, or 3 V. We can use the formula for the charging of a capacitor in an RC circuit:

V = V0(1 - e^(-t/RC))

where V0 is the voltage of the battery, t is the time, R is the resistance, and C is the capacitance. We can rearrange this equation to solve for the time:

t = -RC ln(1 - V/V0)

Plugging in the given values, we get:

t = -(5.0 x 10^6 Ω)(6.0 x 10^-6 F) ln(1 - 3/15)

t = 1.85 x 10^6 s

Now that we have the time, we can use the formula for the current in the circuit:

I = V/R e^(-t/RC)

Plugging in the given values, we get:

I = (15 V)/(5.0 x 10^6 Ω) e^(-1.85 x 10^6 s/(5.0 x 10^6 Ω)(6.0 x 10^-6 F))

I ≈ 2.4 μA

Therefore, the best choice is B.

Question 10

RC circuits: An uncharged 1.0-μF capacitor is connected in series with a  resistor, an ideal  battery, and an open switch. What is the voltage across the capacitor  after closing the switch?

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Question 11

Meters: A galvanometer has an internal resistance of 100 Ω and deflects full-scale at a current of 2.00 mA. What size resistor should be added to it to convert it to a millivoltmeter capable of reading up to 400 mV, and how should this resistor be connected to the galvanometer?

Accepted Answer

To convert a galvanometer to a millivoltmeter with a full-scale deflection at 400 mV, the total resistance needed for the circuit can be calculated using Ohm's law (V = IR), where V is the voltage (400 mV or 0.4 V), and I is the current (2.00 mA or 0.002 A). The total resistance required is V/I = 0.4 V / 0.002 A = 200 Ω. Since the galvanometer already has an internal resistance of 100 Ω, an additional 100 Ω resistor is needed in series to achieve the total resistance of 200 Ω.

Question 12

RC circuits: For the circuit shown in the figure, the switch S is initially open and the capacitor voltage is 80 V. The switch is then closed at time t = 0. What is the charge on the capacitor when the current in the circuit is 33 μA?

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Question 13

Meters: A galvanometer has a coil with a resistance of 24.0 Ω, and a current of 180 μA causes it to deflect full scale. If this galvanometer is to be used to construct an ammeter that can read up to 10.0 A, what shunt resistor is required?

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Question 14

RC circuits: A 4.0-mF capacitor is discharged through a 4.0-kΩ resistor. How long will it take for the capacitor to lose half its initial stored energy?

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Quiz 22: Gausss Law

Meters: A galvanometer has an internal resistance of 100 Ω and deflects full-scale at 2.00 mA. What size resistor should be added to the galvanometer to convert it to a milliammeter capable of reading up to 4.00 mA, and how should this resistor be connected to the galvanometer?

RC circuits: For the circuit shown in the figure, the switch S is initially open and the capacitor voltage is 80 V. The switch is then closed at time t = 0. How long after closing the switch will the current in the resistor be 7.0 µA?

Meters: In the circuit shown in the figure, two 360.0-Ω resistors are connected in series with an ideal source of emf. A voltmeter with internal resistance of 6350 Ω is connected across one of the resistors and reads 3.23 V. Find the emf of the source.

RC circuits: A 4.0-μF capacitor that is initially uncharged is connected in series with a 4.0-kΩ resistor and an ideal 17.0-V battery. How much energy is stored in the capacitor 17 ms after the battery has been connected?

Meters: A galvanometer with a resistance of 40.0 Ω deflects full scale at a current of 2.0 mA. What resistance should be used with this galvanometer in order to construct a voltmeter that can read a maximum of 50 V?

RC circuits: For the circuit shown in the figure, the switch S is initially open and the capacitor is uncharged. The switch is then closed at time t = 0. How many seconds after closing the switch will the energy stored in the capacitor be equal to 50.2 mJ?

RC circuits: A 6.0-μF capacitor is connected in series with a 5.0 MΩ resistor, and this combination is connected across an ideal 15-V DC battery. What is the current in the circuit when the capacitor has reached 20% of its maximum charge?

RC circuits: An uncharged 1.0-μF capacitor is connected in series with a resistor, an ideal battery, and an open switch. What is the voltage across the capacitor after closing the switch?

Meters: A galvanometer has an internal resistance of 100 Ω and deflects full-scale at a current of 2.00 mA. What size resistor should be added to it to convert it to a millivoltmeter capable of reading up to 400 mV, and how should this resistor be connected to the galvanometer?

RC circuits: For the circuit shown in the figure, the switch S is initially open and the capacitor voltage is 80 V. The switch is then closed at time t = 0. What is the charge on the capacitor when the current in the circuit is 33 μA?

Meters: A galvanometer has a coil with a resistance of 24.0 Ω, and a current of 180 μA causes it to deflect full scale. If this galvanometer is to be used to construct an ammeter that can read up to 10.0 A, what shunt resistor is required?

RC circuits: A 4.0-mF capacitor is discharged through a 4.0-kΩ resistor. How long will it take for the capacitor to lose half its initial stored energy?