Find out the inductance of an inductor which should be connected in series with a capacitor of `5muF`,a resistance of `10Omega` and an ac source of 50 Hz so that the power factor of the circuit is 1.

Explanation

To find the inductance of an inductor that should be connected in series with a capacitor of \(5 \mu F\), a resistance of \(10 \Omega\), and an AC source of \(50 Hz\) such that the power factor of the circuit is \(1\), we can follow these steps:

### Step 1: Understand the condition for power factor
The power factor \( \cos \phi \) is given by the formula:
\[ \cos \phi = \frac{R}{Z} \]
where \( R \) is the resistance and \( Z \) is the impedance of the circuit. For a power factor of \(1\), we have:
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