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An alternating current with a peak value of 5A passes through a resistor of resistance...

Physics
WAEC 1997

An alternating current with a peak value of 5A passes through a resistor of resistance 10Ω. Calculate the rate at which energy is dissipated in the resistor

  • A. 250W
  • B. 125W
  • C. 50W
  • D. 35.4W
  • E. 12.5W
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Correct Answer: Option B
Explanation

Given: Peak current, \( I_{\text{peak}} = 5 \, \text{A} \),  Resistance, \( R = 10 \, \Omega \)

Calculate the rms current: The rms current is given by:
\(I_{\text{rms}} = \frac{I_{\text{peak}}}{\sqrt{2}} = \frac{5}{\sqrt{2}} \approx 3.54 \, \text{A}\)

Calculate the power dissipated in the resistor: Using the rms value, the power can be calculated as:
\(P = I_{\text{rms}}^2 \cdot R\)
Substituting the values:
\(P = \left(\frac{5}{\sqrt{2}}\right)^2 \cdot 10\)
Calculating:
\(P = \frac{25}{2} \cdot 10 = 125 \, \text{W}\).


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