A power of 180 WW is delivered to a certain resistor when the applied voltage is 100 V
The correct answer and explanation is:
To find the resistance of the resistor, use the power formula: P=V2RP = \frac{V^2}{R}
Where:
- PP is the power in watts (W)
- VV is the voltage in volts (V)
- RR is the resistance in ohms (Ω)
Given:
Power P=180 WP = 180 \, \text{W}
Voltage V=100 VV = 100 \, \text{V}
Substitute the known values into the formula: 180=1002R180 = \frac{100^2}{R} 180=10000R180 = \frac{10000}{R}
Multiply both sides by RR: 180R=10000180R = 10000
Divide both sides by 180: R=10000180≈55.56 ohmsR = \frac{10000}{180} \approx 55.56 \, \text{ohms}
Correct Answer: The resistance is approximately 55.56 ohms.
Explanation (300 words):
Electrical power is the rate at which energy is used or produced in a circuit. The formula that relates power, voltage, and resistance is derived from Ohm’s Law and the basic power equation. Power PP can be calculated using the formula P=V×IP = V \times I, where VV is voltage and II is current. Substituting Ohm’s Law I=VRI = \frac{V}{R} into the power equation gives P=V2RP = \frac{V^2}{R}.
In this case, the question provides the amount of power consumed by the resistor and the voltage across it. Using the formula P=V2RP = \frac{V^2}{R}, one can rearrange it to solve for resistance by multiplying both sides by RR and then dividing both sides by PP, leading to R=V2PR = \frac{V^2}{P}.
Substituting the given values of voltage (100 volts) and power (180 watts) into the formula gives R=1002180R = \frac{100^2}{180}, which simplifies to R=10000180R = \frac{10000}{180}. The result is approximately 55.56 ohms. This value represents the amount of resistance required to limit the current flow so that the power delivered stays at 180 watts with the applied voltage of 100 volts.
Understanding this concept is crucial in designing and analyzing electric circuits to ensure components are not damaged by excess current or power.