In an A.C circuit whene fresuancy is 60 Hz the volt across an inductor coll is 12 Urms and the of current flowing is 0.1 Arms. Calcaldo the inductanca

To calculate the inductance in an AC circuit, we can use the formula: \[ L = \frac{V_{rms}}{I_{rms} \times \omega} \] where: - \( L \) is the inductance, - \( V_{rms} \) is the root mean square voltage across the inductor, - \( I_{rms} \) is the root mean square current flowing through the inductor, - \( \omega \) is the angular frequency of the AC circuit. Given: - \( V_{rms} = 12 \, \text{V} \), - \( I_{rms} = 0.1 \, \text{A} \), - \( \omega = 2 \pi f = 2 \pi \times 60 \, \text{rad/s} \). Substitute the given values into the formula to calculate the inductance. Calculate the value by following steps: - step0: Calculate: \(\frac{12}{\left(0.1\times 2\times 3.14159\times 60\right)}\) - step1: Remove the parentheses: \(\frac{12}{0.1\times 2\times 3.14159\times 60}\) - step2: Multiply the terms: \(\frac{12}{37.69908}\) - step3: Convert the expressions: \(\frac{12}{\frac{942477}{25000}}\) - step4: Multiply by the reciprocal: \(12\times \frac{25000}{942477}\) - step5: Reduce the numbers: \(4\times \frac{25000}{314159}\) - step6: Multiply: \(\frac{4\times 25000}{314159}\) - step7: Multiply: \(\frac{100000}{314159}\) The inductance in the AC circuit is approximately 0.31831 H.