AP Physics Questions on Resistors in Series and Parallel

📚 Quick Study Guide

• ➕ Resistors in Series: The total resistance ($R_{total}$) is the sum of individual resistances: $R_{total} = R_1 + R_2 + R_3 + ...$ The current is the same through each resistor.
• ➗ Resistors in Parallel: The reciprocal of the total resistance is the sum of the reciprocals of individual resistances: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$ The voltage is the same across each resistor.
• 💡 Ohm's Law: Relates voltage (V), current (I), and resistance (R): $V = IR$
• ⚡ Power Dissipation: The power (P) dissipated by a resistor is given by: $P = I^2R = \frac{V^2}{R} = IV$
• 📏 Voltage Divider (Series): The voltage across a resistor in a series circuit is proportional to its resistance: $V_x = V_{total} \cdot \frac{R_x}{R_{total}}$
• 🔄 Current Divider (Parallel): The current through a resistor in a parallel circuit is inversely proportional to its resistance: $I_x = I_{total} \cdot \frac{R_{total}}{R_x}$, where $R_{total}$ is the equivalent resistance of the parallel combination.

🧪 Practice Quiz

1. What is the total resistance of three resistors with values 10 $\Omega$, 20 $\Omega$, and 30 $\Omega$ connected in series?
   1. 10 $\Omega$
   2. 20 $\Omega$
   3. 30 $\Omega$
   4. 60 $\Omega$
2. What is the total resistance of two resistors with values 4 $\Omega$ and 4 $\Omega$ connected in parallel?
   1. 8 $\Omega$
   2. 0.25 $\Omega$
   3. 2 $\Omega$
   4. 16 $\Omega$
3. A 6 $\Omega$ and a 12 $\Omega$ resistor are connected in parallel. If the voltage across the 6 $\Omega$ resistor is 12 V, what is the current through the 12 $\Omega$ resistor?
   1. 1 A
   2. 2 A
   3. 3 A
   4. 4 A
4. Three resistors of 3 $\Omega$, 6 $\Omega$, and 9 $\Omega$ are connected in series to a 18 V battery. What is the current flowing through the circuit?
   1. 0.5 A
   2. 1 A
   3. 1.5 A
   4. 2 A
5. A 10 $\Omega$ and a 15 $\Omega$ resistor are connected in parallel. If a total current of 5 A flows into the parallel combination, what is the current flowing through the 10 $\Omega$ resistor?
   1. 1 A
   2. 2 A
   3. 3 A
   4. 4 A
6. A series circuit consists of a 12 V battery and two resistors, 4 $\Omega$ and 2 $\Omega$. What is the voltage drop across the 4 $\Omega$ resistor?
   1. 4 V
   2. 6 V
   3. 8 V
   4. 12 V
7. Two resistors, 5 $\Omega$ and 20 $\Omega$, are connected in parallel to a voltage source. If the total power dissipated in the circuit is 100 W, what is the voltage of the source?
   1. 10 V
   2. 20 V
   3. 40 V
   4. 50 V