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

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

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

Answer: (B)

In parallel, the same voltage from the source applies to every branch, so each resistor sees 24 volts across it. The total power from the source is the sum of the power in each resistor, and since the two resistors are equal, each resistor dissipates the same amount of power, making the total power twice the power of one resistor. A single resistor with 24 volts across it dissipates P = V^2 / R, so the total power is 48 = 2*(24^2 / R). That gives 48 = 1152 / R, so R = 1152 / 48 = 24 ohms. Another way to see it: the total equivalent resistance is R_eq = V^2 / P = 576 / 48 = 12 ohms. For two equal resistors in parallel, R_eq = R/2, so R/2 = 12, giving R = 24 ohms. Therefore, each resistor is 24 ohms.

In parallel, the same voltage from the source applies to every branch, so each resistor sees 24 volts across it. The total power from the source is the sum of the power in each resistor, and since the two resistors are equal, each resistor dissipates the same amount of power, making the total power twice the power of one resistor. A single resistor with 24 volts across it dissipates P = V^2 / R, so the total power is 48 = 2*(24^2 / R). That gives 48 = 1152 / R, so R = 1152 / 48 = 24 ohms.

Another way to see it: the total equivalent resistance is R_eq = V^2 / P = 576 / 48 = 12 ohms. For two equal resistors in parallel, R_eq = R/2, so R/2 = 12, giving R = 24 ohms.

Therefore, each resistor is 24 ohms.