Question

An inductive coil consumes 500w of power at 10a and 110v and 60hz.The inductance of the coil is

Answer 1

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Answer 2

Concept

Power is defined because the rate at which work is completed upon an object. Power could be a time-based quantity.

Given

We are on condition that an inductive coil consumes the ability of $500W$ with current $10a$ at a voltage $110v$ and also the frequency is $60hz.$

Find

We have to search out the inductance of the coil.

Solution

Firstly, we are going to find the worth of impedance using the formula $Z=R+jX_{L}$.

$\begin{aligned}R+jX_{L}&=\frac{V_{S}}{I}\\ &=\frac{110}{10}\\ &=11\end{aligned}$

Now, we are going to find the complex power using the formula $S=VI^{*}$.

$\begin{aligned}S&=110\times 10\\ &=1100\end{aligned}$

Further, we are going to substitute the values in $S=P+jQ$, we get

$\begin{aligned}P+jQ&=1100\\ 500+jQ&=1100\\ jQ&=600\end{aligned}$

Now, we are going to substitute $jQ=I^2 2\pi fL$, we get

$\begin{aligned}(10)^2 2\pi fL&=1100\\ 2\pi fL&=6\\ L&=\frac{6}{2\pi(60)}\\ L&=0.015915H\end{aligned}$

Hence, the inductance of coil is$L=0.015915H$ or $L=15.915mH$.

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