In a series circuit, if Resistor A has three times the resistance of Resistor B, the voltage across Resistor A will be what relative to the voltage across Resistor B?

In a series circuit, if Resistor A has three times the resistance of Resistor B, the voltage across Resistor A will be what relative to the voltage across Resistor B?

• A. 1/3
• B. 2/3
• C. 3 times
• D. the same as

Answer: (C)

In a series circuit the same current flows through every component, and the voltage drop across each resistor is proportional to its resistance (V = IR). If Resistor A has three times the resistance of Resistor B, the current I is the same for both, so V_A = I × R_A = I × (3 × R_B) = 3 × (I × R_B) = 3 × V_B. So the voltage across A is three times the voltage across B. For a quick check, imagine B has 2 ohms and A has 6 ohms; with the same current, V_B = 2I and V_A = 6I, which is three times V_B.

In a series circuit the same current flows through every component, and the voltage drop across each resistor is proportional to its resistance (V = IR). If Resistor A has three times the resistance of Resistor B, the current I is the same for both, so V_A = I × R_A = I × (3 × R_B) = 3 × (I × R_B) = 3 × V_B. So the voltage across A is three times the voltage across B. For a quick check, imagine B has 2 ohms and A has 6 ohms; with the same current, V_B = 2I and V_A = 6I, which is three times V_B.