Question

# A coil of inductance 0.5 h and a resistor of resistance 100ω are connected in series to a 240v,50 hz supply. (a) find the maximum current in the circuit (b) what is the time lag between voltage maximum and current maximum?

Open in App
Solution

## Step 1: GivenInductance, L = 0.5HResistance, $R=100\Omega$RMS voltage,${V}_{rms}=240v$Frequency, f = 50HzStep 2: Calculate impedance for LR circuitangular frequency, $\omega =2\pi f$Substitute values-$\omega =2\pi ×50\phantom{\rule{0ex}{0ex}}\omega =100\pi rad/s$Inductive reactance, ${X}_{L}=\omega L$Substitute values-${X}_{L}=100\pi ×0.5\phantom{\rule{0ex}{0ex}}{X}_{L}=50\pi$Now, the impedance for LR circuit, $z=\sqrt{{X}_{L}^{2}+{R}^{2}}$Substitute values-$z=\sqrt{{\left(50\pi \right)}^{2}+{100}^{2}}\phantom{\rule{0ex}{0ex}}z=186.142\Omega$Step 3: Calculate the Maximum Current In The CircuitAccording to ohms law for AC, ${V}_{rms}=z.{I}_{rms}$, here ${I}_{rms}$ is the RMS current.Substitute values-$240=186.142×{I}_{rms}\phantom{\rule{0ex}{0ex}}{I}_{rms}=1.289A$Also, ${I}_{rms}=\frac{{I}_{max}}{\sqrt{2}}\phantom{\rule{0ex}{0ex}}{I}_{max}={I}_{rms}\sqrt{2}$here ${I}_{max}$ is the maximum current.Substitute values-${I}_{max}=1.289\sqrt{2}\phantom{\rule{0ex}{0ex}}{I}_{max}=1.289×1.414\phantom{\rule{0ex}{0ex}}{I}_{max}=1.8226A$thus, the The Maximum Current In The Circuit is $1.8226A$.Step 4: Calculate the Time Lag Between Voltage Maximum And Current Maximum$\mathrm{cos}\varphi =\frac{R}{z}\phantom{\rule{0ex}{0ex}}\mathrm{cos}\varphi =\frac{100}{186.142}\phantom{\rule{0ex}{0ex}}\varphi ={\mathrm{cos}}^{-1}\left(\frac{100}{186.142}\right)\phantom{\rule{0ex}{0ex}}\varphi =1radian$now, the time lag, $t=\frac{\varphi }{\omega }\phantom{\rule{0ex}{0ex}}t=\left(\frac{1}{100\pi }\right)s\phantom{\rule{0ex}{0ex}}$.Thus, the time lag is $\left(\frac{1}{100\pi }\right)s\phantom{\rule{0ex}{0ex}}$.Hence,(A) The Maximum Current In The Circuit is $1.8226A$.(B) The Time Lag Between Voltage Maximum And Current Maximum is $\left(\frac{1}{100\pi }\right)s\phantom{\rule{0ex}{0ex}}$.

Suggest Corrections
1
Explore more