Q: In the circuit shown (first image), what is the value of the EMF $$\mathcal{E}_1$$ required to satisfy the loop rule for loop 1 (containing the 4 $$\Omega$$ and 3 $$\Omega$$ resistors)?

$$\mathcal{E}_1 = 36\ \text{V}$$

Q: For loop 2 in the first circuit, what is the value of the EMF $$\mathcal{E}_2$$?

$$\mathcal{E}_2 = 54\ \text{V}$$

Q: How much power is supplied by the live battery in the second circuit?

$$P_{\text{live}} = 5.50\ \text{W}$$

Q: How much power is absorbed by the dead battery in the second circuit?

$$P_{\text{dead}} = 3.00\ \text{W}$$

Q: What is the power dissipated in the 3 $$\Omega$$ resistor in the second circuit?

$$P_{3\Omega} = 0.75\ \text{W}$$

Q: What is the power dissipated in the 7 $$\Omega$$ resistor in the second circuit?

$$P_{7\Omega} = 1.75\ \text{W}$$

Question 1

In the circuit shown (first image), what is the value of the EMF $$\mathcal{E}_1$$ required to satisfy the loop rule for loop 1 (containing the 4 $$\Omega$$ and 3 $$\Omega$$ resistors)?

Accepted Answer

$$\mathcal{E}_1 = 36\ 	ext{V}$$

Question 2

Using Kirchhoff’s junction rule at point P in the first circuit, what is the value of the current $$I$$ through the 3 $$\Omega$$ resistor?

Accepted Answer

$$I = -8\ 	ext{A}$$

Question 3

For loop 2 in the first circuit, what is the value of the EMF $$\mathcal{E}_2$$?

Accepted Answer

$$\mathcal{E}_2 = 54\ 	ext{V}$$

Question 4

In the first circuit, what is the value of the unknown resistor $$R$$?

Accepted Answer

$$R = 9\ \Omega$$

Question 5

In the second circuit (with two batteries), what is the current $$I in $$the loop?

Accepted Answer

$$I = 0.50\ 	ext{A}$$

Question 6

What is the potential difference $$V_a - V_b in $$the second circuit?

Accepted Answer

$$V_a - V_b = 9.50\ 	ext{V}$$

Question 7

How much power is supplied by the live battery in the second circuit?

Accepted Answer

$$P_{	ext{live}} = 5.50\ 	ext{W}$$

Question 8

How much power is absorbed by the dead battery in the second circuit?

Accepted Answer

$$P_{	ext{dead}} = 3.00\ 	ext{W}$$

Question 9

What is the power dissipated in the 3 $$\Omega$$ resistor in the second circuit?

Accepted Answer

$$P_{3\Omega} = 0.75\ 	ext{W}$$

Question 10

What is the power dissipated in the 7 $$\Omega$$ resistor in the second circuit?

Accepted Answer

$$P_{7\Omega} = 1.75\ 	ext{W}$$

Question 11

In the charging capacitor circuit, what is the initial current $$i(0)$$ immediately after closing the switch?

Accepted Answer

$$i(0) = \frac{\mathcal{E}}{R}$$

Question 12

For a charging capacitor, what is the final charge $$q(\infty) on $$the capacitor?

Accepted Answer

$$q(\infty) = \mathcal{E} C$$

Question 13

What is the time constant $$	au$$ for the charging capacitor circuit?

Accepted Answer

$$	au = RC$$

Question 14

What is the energy stored in the capacitor when fully charged?

Accepted Answer

$$U = \frac{1}{2} C \mathcal{E}^2$$

Question 15

At what time is the energy stored in the capacitor half its maximum value?

Accepted Answer

$$t = -RC \ln(0.293)$$

Question 16

If the current in a charging capacitor circuit has dropped to $$\frac{1}{5} of $$its initial value, what is the charge on the capacitor at that time?

Accepted Answer

$$q(t) = \frac{4}{5} \mathcal{E} C$$

Question 17

In a real-world scenario, why is the time constant $$	au = RC$$ important in medical defibrillators?

Accepted Answer

It determines how quickly the capacitor can discharge to deliver a shock.

Kirchhoff’s Laws and RC Circuits: Study Notes for Physics with Calculus

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