In a 24-volt source delivering 48 watts to a parallel circuit consisting of two equal resistors, what is the value of each resistor?

In a 24-volt source delivering 48 watts to a parallel circuit consisting of two equal resistors, what is the value of each resistor?

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

Answer: (C)

In a parallel circuit, the voltage across each resistor is the same as the source, and two identical resistors in parallel give an equivalent resistance that is half of one resistor. Use P = V^2 / R_eq to find the overall resistance from the given power and voltage. With a 24-volt source delivering 48 watts, the total (equivalent) resistance is R_eq = 24^2 / 48 = 12 ohms. Since two equal resistors are in parallel, R_eq = R / 2, so R = 2 × 12 = 24 ohms. A quick check: the current from the source is I = V / R_eq = 24 / 12 = 2 A, and P = V × I = 24 × 2 = 48 W, which matches. Each resistor is 24 ohms.

In a parallel circuit, the voltage across each resistor is the same as the source, and two identical resistors in parallel give an equivalent resistance that is half of one resistor. Use P = V^2 / R_eq to find the overall resistance from the given power and voltage. With a 24-volt source delivering 48 watts, the total (equivalent) resistance is R_eq = 24^2 / 48 = 12 ohms. Since two equal resistors are in parallel, R_eq = R / 2, so R = 2 × 12 = 24 ohms. A quick check: the current from the source is I = V / R_eq = 24 / 12 = 2 A, and P = V × I = 24 × 2 = 48 W, which matches. Each resistor is 24 ohms.