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

A. 36 ohms.
B. 4 ohms.
C.12 ohms.

1 Answer

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Final answer:

In a parallel circuit with a 48-volt source and a total power consumption of 192 watts, each resistor has a value of 36 ohms.

Step-by-step explanation:

In a parallel circuit, the total power is equal to the sum of the power dissipated by each individual resistor. Therefore, we can use the formula P = VI, where P is the power, V is the voltage, and I is the current.

Given that the source voltage is 48 volts, and the total power is 192 watts, we can find the total current by dividing the power by the voltage: I = P / V = 192 / 48 = 4 amps.

Since the circuit consists of three equal resistors, we can divide the total current evenly among them. Therefore, the current passing through each resistor is 4 amps / 3 = 1.333 amps.

Using Ohm's law, we can find the value of each resistor by dividing the voltage across each resistor by the current passing through it. Since the voltage across each resistor is equal to the source voltage, the resistance of each resistor is equal to the voltage divided by the current: R = V / I = 48 / 1.333 = 36 ohms.

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