What resistance is indicated when a circuit with a current of 12 amps operates with a power consumption of 1440 watts?

What resistance is indicated when a circuit with a current of 12 amps operates with a power consumption of 1440 watts?

• A. 5 Ohms
• B. 10 Ohms
• C. 12 Ohms
• D. 15 Ohms

Answer: (B)

To determine the resistance in the circuit, we can use the formulas related to power, voltage, current, and resistance. The power consumed in an electrical circuit is given by the equation: \[ P = I^2 \cdot R \] where \( P \) is the power in watts, \( I \) is the current in amps, and \( R \) is the resistance in ohms. Given that the power (P) is 1440 watts and the current (I) is 12 amps, we can rearrange the formula to solve for resistance (R): \[ R = \frac{P}{I^2} \] First, we calculate \( I^2 \): \[ I^2 = 12^2 = 144 \] Now we can substitute this value back into the equation for resistance: \[ R = \frac{1440}{144} = 10 \text{ ohms} \] This calculation yields a resistance of 10 ohms, which is the correct value. The relationship between power, current, and resistance clearly indicates how they interact in a circuit. The other options do not correspond to the calculations derived from the power and current values provided, demonstrating that they do not represent

To determine the resistance in the circuit, we can use the formulas related to power, voltage, current, and resistance. The power consumed in an electrical circuit is given by the equation:

[ P = I^2 \cdot R ]

where ( P ) is the power in watts, ( I ) is the current in amps, and ( R ) is the resistance in ohms.

Given that the power (P) is 1440 watts and the current (I) is 12 amps, we can rearrange the formula to solve for resistance (R):

[ R = \frac{P}{I^2} ]

First, we calculate ( I^2 ):

[ I^2 = 12^2 = 144 ]

Now we can substitute this value back into the equation for resistance:

[ R = \frac{1440}{144} = 10 \text{ ohms} ]

This calculation yields a resistance of 10 ohms, which is the correct value. The relationship between power, current, and resistance clearly indicates how they interact in a circuit.

The other options do not correspond to the calculations derived from the power and current values provided, demonstrating that they do not represent