Single-Phase AC Circuits Quiz
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Questions and Answers

What is the expression for current drawn in a purely resistive circuit when a sinusoidal voltage of $v = V_m imes ext{sin}( ext{ω}t)$ is applied?

  • $i = V_m \times \text{cos}(\text{ω}t)$
  • $i = \frac{V_m}{R} \times \text{sin}(\text{ω}t)$ (correct)
  • $i = \frac{V_m}{R} \times \text{cos}(\text{ω}t)$
  • $i = V_m \times \text{sin}(\text{ω}t)$
  • What is the average power consumed in a purely resistive circuit with a sinusoidal voltage of $v = V_m \times \text{sin}(\text{ω}t)$?

  • $P = V_m \times I_m \times \text{cos}(2\text{ω}t)$
  • $P = \frac{V_m \times I_m}{2} \times \text{cos}(2\text{ω}t)$
  • $P = V_m \times I_m$
  • $P = \frac{V_m \times I_m}{2}$ (correct)
  • What is the instantaneous power in a purely resistive circuit with a sinusoidal voltage of $v = V_m \times \text{sin}(\text{ω}t)$?

  • $p = V_m \times I_m \times (1 - \text{cos}(2\text{ω}t))$ (correct)
  • $p = V_m \times I_m \times (1 - \text{cos}(\text{ω}t))$
  • $p = V_m \times I_m \times \text{sin}(2\text{ω}t)$
  • $p = V_m \times I_m \times \text{sin}^2(\text{ω}t)$
  • At what point is the current maximum in a purely resistive circuit with a sinusoidal voltage of $v = V_m \times \text{sin}(\text{ω}t)$?

    <p>When $\text{sin}(\text{ω}t)$ is unity</p> Signup and view all the answers

    What is the expression for current drawn in a purely resistive circuit when a sinusoidal voltage of $v = V_m \times \text{cos}(\text{ω}t)$ is applied?

    <p>$i = \frac{V_m}{R} \times \text{cos}(\text{ω}t)$</p> Signup and view all the answers

    Study Notes

    Sinusoidal Voltage in a Purely Resistive Circuit

    • The current drawn in a purely resistive circuit with a sinusoidal voltage of $v = V_m \times \text{sin}(\text{ω}t)$ is expressed as $i = I_m \times \text{sin}(\text{ω}t)$.
    • The average power consumed in a purely resistive circuit with a sinusoidal voltage is $P_{avg} = \frac{V_m^2}{2R}$.
    • The instantaneous power in a purely resistive circuit with a sinusoidal voltage is $p = \frac{V_m^2}{R} \times \text{sin}^2(\text{ω}t)$.
    • The current is maximum in a purely resistive circuit with a sinusoidal voltage when $\text{ω}t = \frac{\pi}{2} + k\pi$, where $k$ is an integer.
    • The current drawn in a purely resistive circuit with a sinusoidal voltage of $v = V_m \times \text{cos}(\text{ω}t)$ is expressed as $i = I_m \times \text{cos}(\text{ω}t)$.

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    Description

    Test your knowledge of single-phase AC circuits with this quiz on the foundations of electrical engineering. Explore the derivation of current and power consumption in a purely resistive circuit when a sinusoidal voltage is applied. Delve into circuit diagrams, V&I waveforms, and phasor diagrams. Ideal for first-year BTECH students at JSPM University.

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