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Chapter 21: Problem 72

A capacitor is rated at \(0.025 \mu \mathrm{F}\). How much rms current flows when the capacitor is connected to a \(110-\mathrm{V}\) rms, \(60.0-\mathrm{Hz}\) line?

Short Answer

Expert verified
Based on the given information, the problem required finding the rms current flowing through a capacitor connected to an AC voltage source. To solve this, we first calculated the capacitive reactance using the formula \(X_C = \frac{1}{2\pi fC}\) and found it to be approximately \(106.22 \Omega\). Then, we used Ohm's law for AC circuits (\(I = \frac{V}{X_C}\)) to find the rms current, which was approximately \(1.036 A\).

Step by step solution

01

Calculate the capacitive reactance

We need to determine the capacitive reactance, denoted as \(X_C\), which can be calculated using the formula: \(X_C = \frac{1}{2\pi fC}\). Here, \(f\) represents the frequency of the AC source and \(C\) represents the capacitance. Plugging in the given values, we have: \(X_C = \frac{1}{2\pi (60.0Hz)(0.025\mu F)}\) Convert the capacitance in farads: \(0.025\mu F = 0.025 \times 10^{-6} F\) Now, calculate \(X_C\): \(X_C = \frac{1}{2\pi (60Hz)(0.025 \times 10^{-6} F)} \approx 106.22 \Omega\)
02

Calculate the rms current using Ohm's law for AC circuits

Ohm's law states that \(I = \frac{V}{X_C}\), where \(I\) is the rms current, \(V\) is the rms voltage, and \(X_C\) is the capacitive reactance calculated in step 1. Plugging in the values, we get: \(I = \frac{110V}{106.22 \Omega} \approx 1.036 A\) Therefore, the rms current flowing through the capacitor is approximately \(1.036 A\).

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Most popular questions from this chapter

The voltage across an inductor and the current through the inductor are related by \(v_{\mathrm{L}}=L \Delta i / \Delta t .\) Suppose that $i(t)=I \sin \omega t .\( (a) Write an expression for \)v_{\mathrm{L}}(t) .$ [Hint: Use one of the relationships of Eq. \((20-7) .]\) (b) From your expression for \(v_{\mathrm{L}}(t),\) show that the reactance of the inductor is \(X_{\mathrm{L}}=\omega L_{\mathrm{r}}\) (c) Sketch graphs of \(i(t)\) and \(v_{\mathrm{L}}(t)\) on the same axes. What is the phase difference? Which one leads?
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