A 24-volt source is used to supply 48 watts to a parallel circuit consisting of two resistors of equal value. What is the resistance of each resistor?

A 24-volt source is used to supply 48 watts to a parallel circuit consisting of two resistors of equal value. What is the resistance of each resistor?

• A. 12 ohms
• B. 48 ohms
• C. 24 ohms
• D. 6 ohms

Answer: (C)

In a parallel circuit, the full source voltage appears across every branch, and with two identical resistors, each branch dissipates the same amount of power. The total power drawn from the source is the sum of the powers in both branches, so each resistor shares half of the total power. Use P = V^2 / R for one resistor. The total power is 48 W, so each resistor uses half of that, but since both see the same voltage, you can set up 48 = 2 × (24^2 / R). Solving gives R = (2 × 576) / 48 = 24 ohms for each resistor. You can also check by looking at equivalent resistance: two equal resistors in parallel have R_eq = R / 2. The source power is P = V^2 / R_eq, so 48 = 24^2 / (R/2) leads to R/2 = 12 ohms, hence R = 24 ohms.

In a parallel circuit, the full source voltage appears across every branch, and with two identical resistors, each branch dissipates the same amount of power. The total power drawn from the source is the sum of the powers in both branches, so each resistor shares half of the total power.

Use P = V^2 / R for one resistor. The total power is 48 W, so each resistor uses half of that, but since both see the same voltage, you can set up 48 = 2 × (24^2 / R). Solving gives R = (2 × 576) / 48 = 24 ohms for each resistor.

You can also check by looking at equivalent resistance: two equal resistors in parallel have R_eq = R / 2. The source power is P = V^2 / R_eq, so 48 = 24^2 / (R/2) leads to R/2 = 12 ohms, hence R = 24 ohms.