# Alternating Current

## Physics

### NCERT

1   A $100\Omega$ resistor is connected to a $220 V,50 Hz$ ac supply.$\\$ (a) What is the rms value of current in the circuit?$\\$ (b) What is the net power consumed over a full cycle?

Given:$\\$ $R=100 \text{ohms}\\ V=220V$$\\ Frequency(f) =50 Hz \\ (a) We know \\ I_{rms}=\dfrac{V_{rms}}{R}$$\\$ Substituting the values $\\$ $I_{rms}=\dfrac{220}{100}=2.20A$$\\ (b)Power=V.I$$\\$ Or Power=$220*2.2$$\\ Or Power=484 W 2 a) The peak voltage of an ac supply is 300 V. What is the rms voltage?\\ b) The rms value of current in an ac circuit is 10 A. What is the peak current? ##### Solution : a) Peak voltage of the ac supply, V _0 =300 V$$\\$ We know $V_{rms}=\dfrac{V_0}{\sqrt{2}}\\ =\dfrac{300}{\sqrt{2}}=212.1V$$\\ b) The rms value of current is given as I=10 A$$\\$ Using above identity for current peak current is given as:$\\$ $I_0=1.414*I_{rms}\\ \text{Or } I_0=1.414*10=14.14 A$

3   A $44 mH$ inductor is connected to $220 V, 50 Hz$ ac supply. Determine the rms value of the current in the circuit.