AP Physics 2: Algebra-Based Practice Quiz: Compound Direct Current (DC) Circuits

Correct Answer: C

According to the provided content, the equivalent resistance of a set of resistors in series is the sum of the individual resistances. Therefore, R_eq = 2 Ω + 4 Ω + 6 Ω = 12 Ω.

Correct Answer: C

The provided content defines a series connection as one in which any charge passing through one circuit element must proceed through all elements in that connection and has no other path available.

Correct Answer: B

For resistors in parallel, the inverse of the equivalent resistance is the sum of the inverses of the individual resistances. 1/R_eq = 1/10 Ω + 1/15 Ω = 3/30 Ω + 2/30 Ω = 5/30 Ω = 1/6 Ω. Therefore, R_eq = 6 Ω.

Correct Answer: B

The provided content explicitly states that ammeters must be connected in series with the element in which current is being measured.

Correct Answer: B

The provided content states that voltmeters must be connected in parallel with the element across which potential difference is being measured.

Correct Answer: C

The content specifies that the internal resistance of a nonideal battery may be treated as the resistance of a resistor in series with an ideal battery and the remainder of the circuit.

Correct Answer: D

The content states that for a series connection, the current in each element must be the same because there is only one path for the charge to follow.

Correct Answer: B

Adding a resistor in parallel adds another path for the current. Mathematically, adding another term (1/R_new) to the sum Σ(1/R_i) increases the value of 1/R_eq, which in turn decreases the value of R_eq.

Correct Answer: C

First, calculate the equivalent resistance of the parallel part: 1/R_p = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4. So, R_p = 4 Ω. Then, add the series resistor: R_eq = R_series + R_p = 3 Ω + 4 Ω = 7 Ω.

Correct Answer: C

The internal resistance is in series with the rest of the circuit. As current flows through it, there is a potential drop (V=IR) across it. This reduces the terminal voltage (the potential difference available to the external circuit) to a value less than the battery's ideal EMF.

Correct Answer: D

The provided content gives the relevant equation for resistors in parallel as: The inverse of the equivalent resistance of a set of resistors connected in parallel is equal to the sum of the inverses of the individual resistances, or $\frac{1}{R_{eq,p}}=\sum_{i}\frac{1}{R_i}$.

Correct Answer: D

To measure total current, the ammeter must be in series with the source (the battery) to measure all charge flowing out. To measure potential difference across R2, the voltmeter must be connected in parallel with R2. This combines the rules for both meters.

Correct Answer: C

Let each resistor be R. In series, R_eq,s = R + R + R = 3R. In parallel, 1/R_eq,p = 1/R + 1/R + 1/R = 3/R, so R_eq,p = R/3. Since R/3 is always smaller than 3R for any positive R, the parallel equivalent resistance is smaller.

Correct Answer: A

A single loop means there is only one path for the current, which is the definition of a series circuit. The rule for series resistance is to sum the individual resistances.

Correct Answer: C

The internal resistance of a nonideal battery is treated as a resistor in series with the rest of the circuit. Therefore, the total equivalent resistance of the entire circuit (internal and external) is the sum of the external resistance R and the internal resistance r.

Correct Answer: B

To connect an ammeter in series (as required), the circuit must be physically broken to insert the meter. To connect a voltmeter in parallel, its leads are simply touched to two points in the circuit without breaking the current path.