Q: For the first circuit, if $$I_1 = 2$$\ \text{A}$$, I_2$ = 1\ \text{A}$$, what is the current through $$R_2$$?

$$I_3$$ = $$I_1$$ - $$I_2 = 1$$\ \text{A}$$

Question 1

In the first circuit diagram, which of the following statements about the equivalent resistance is correct?

Accepted Answer

The circuit does not have a single equivalent resistance because it contains two batteries and a shared resistor.

Question 2

Given $$R_1 = B$$\ \Omega$$, R_2$ = 2B\ \Omega$$, $$R_3 = A$$\ \Omega$$, $$\mathcal{E}_1 = 12\ 	ext{V}$$, and $$\mathcal{E}_2 = 9\ 	ext{V}$$, what is the correct expression for the current I_3$ in the middle wire in terms of I_1$ and I_2$?

Accepted Answer

$$I_3$$ = $$I_1$$ - $$I_2$$

Question 3

For the first circuit, which equation correctly represents Kirchhoff’s loop rule for the left loop?

Accepted Answer

$$\mathcal{E}_1 - I_1$ R_1$ - I_3$ R_2$ = 0$$

Question 4

In the second circuit, if $$R_1$$ = $$R_2$$ = $$R_4 = B$$\ \Omega$$, R_3$ = R_5$ = 2B\ \Omega$$, and $$R_6 = A$$\ \Omega$$, what is the correct formula for the equivalent resistance?

Accepted Answer

$$R_{eq} = \left[ \left( R_1$ + R_2$ \right) \parallel \left( R_3$ \parallel R_4$ \right) \right] + R_5$ + R_6$

Question 5

If the total current from the battery in the second circuit is $$I$$, what is the current through $$R_4$$?

Accepted Answer

$$I_{R_4$} = \frac{R_4$}{R_3$ + R_4$} I_{branch}$$, where $$I_{branch} is $$the current entering the parallel branch containing $$R_3$$ and $$R_4$$

Question 6

For the first circuit, what is the correct expression for the voltage across $$R_2$$?

Accepted Answer

$$V_{R_2$} = I_3$ R_2$

Question 7

Which of the following best describes why the equivalent resistance cannot be calculated for the first circuit using only series and parallel rules?

Accepted Answer

Because the circuit contains a resistor shared between two loops with separate batteries.

Question 8

In the first circuit, if $$I_1$$ flows through $$R_1$$, $$I_2$$ flows through $$R_3$$, and $$I_3$$ flows through $$R_2$$, which equation correctly represents the conservation of current at the top junction?

Accepted Answer

$$I_1$$ = $$I_2$$ + $$I_3$$

Question 9

For the second circuit, which equation correctly represents Kirchhoff’s loop rule for the bottom loop containing $$R_5$$ and $$R_6$$?

Accepted Answer

$$\mathcal{E} - I_{R_5$} R_5$ - I_{R_6$} R_6$ = 0$$

Question 10

If the power dissipated in $$R_2 in $$the first circuit is $$P_{R_2$}$$, which formula is correct?

Accepted Answer

$$P_{R_2$} = I_3$^2 R_2$

Question 11

In the second circuit, if $$R_1$$ = $$R_2$$ = $$R_4 = 2$$\ \Omega$$, R_3$ = R_5$ = 4\ \Omega$$, $$R_6 = 1$$\ \Omega$$, and $$\mathcal{E} = 12\ 	ext{V}$$, what is the equivalent resistance?

Accepted Answer

$$R_{eq} = \left[ (2 + 2) \parallel (4 \parallel 2) \right] + 4 + 1$$

Question 12

For the first circuit, if $$R_1 = 3$$\ \Omega$$, R_2$ = 6\ \Omega$$, $$R_3 = 2$$\ \Omega$$, $$\mathcal{E}_1 = 12\ 	ext{V}$$, $$\mathcal{E}_2 = 9\ 	ext{V}$$, what is the voltage across R_2$ if I_3$ = 1\ 	ext{A}$$?

Accepted Answer

$$V_{R_2$} = 6\ 	ext{V}$$

Question 13

In the second circuit, if the current through $$R_5 is$$ $$I_{R_5$}$$, what is the correct formula for the voltage across $$R_5$$?

Accepted Answer

$$V_{R_5$} = I_{R_5$} R_5$

Question 14

For the first circuit, if $$I_1 = 2$$\ 	ext{A}$$, I_2$ = 1\ 	ext{A}$$, what is the current through $$R_2$$?

Accepted Answer

$$I_3$$ = $$I_1$$ - $$I_2 = 1$$\ 	ext{A}$$

Question 15

In the second circuit, which resistor(s) are in parallel?

Accepted Answer

$$R_3$$ and $$R_4$$

Question 16

For the first circuit, which physical law is primarily used to write equations for the loops?

Accepted Answer

Kirchhoff’s Voltage Law

Question 17

In the second circuit, if the battery supplies a total current $$I$$, which resistor receives the full current directly from the battery?

Accepted Answer

$$R_5$$

Question 18

For the first circuit, if $$R_1 = 4$$\ \Omega$$, R_2$ = 8\ \Omega$$, $$R_3 = 2$$\ \Omega$$, $$\mathcal{E}_1 = 10\ 	ext{V}$$, $$\mathcal{E}_2 = 5\ 	ext{V}$$, and I_1$ = 1\ 	ext{A}$$, what is the power dissipated in $$R_1$$?

Accepted Answer

$$P_{R_1$} = 4\ 	ext{W}$$

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