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Single-Phase AC Circuits Quiz

Created by

@FinestNovaculite

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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.