A 48-volt source furnishes 192 watts to a parallel circuit consisting of three equal resistors. What is the value of each resistor?

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Enhance your understanding of the fundamentals of electricity with the AMT General Exam. Study with multiple-choice questions crafted to improve your knowledge and confidence. Prepare effectively for your success!

Multiple Choice

A 48-volt source furnishes 192 watts to a parallel circuit consisting of three equal resistors. What is the value of each resistor?

Explanation:
In a parallel circuit with equal resistors, the total resistance is one-third of a single resistor. The power provided by the source relates to the voltage and the total resistance by P = V^2 / R_total. Compute the total resistance from the given values: R_total = V^2 / P = 48^2 / 192 = 12 ohms. Since three equal resistors are in parallel, R_total = R / 3, so each resistor is R = 3 × 12 = 36 ohms. Quick check: current through each resistor is I = V / R = 48 / 36 ≈ 1.33 A; total current ≈ 4 A; power = V × I = 48 × 4 = 192 W, which matches. Therefore, each resistor is 36 ohms.

In a parallel circuit with equal resistors, the total resistance is one-third of a single resistor. The power provided by the source relates to the voltage and the total resistance by P = V^2 / R_total.

Compute the total resistance from the given values: R_total = V^2 / P = 48^2 / 192 = 12 ohms. Since three equal resistors are in parallel, R_total = R / 3, so each resistor is R = 3 × 12 = 36 ohms.

Quick check: current through each resistor is I = V / R = 48 / 36 ≈ 1.33 A; total current ≈ 4 A; power = V × I = 48 × 4 = 192 W, which matches. Therefore, each resistor is 36 ohms.

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