Class 12 Physics Alternating Current Resistive AC Circuit

Resistive AC Circuit

• In resistive  AC  circuit there will be only resistors and no other circuit elements will  be  present.
• Consider the circuit as shown in the (fig)  below .
• Input AC voltage   V =  Vm sinωt   (equation(1))
• Where Vm = peak value of voltage. It is also known as voltage amplitude.
• Let the EMF of the voltage source = V, then by applying Kirchhoff’s loop law to the circuit, total EMF  of the circuit will be V = IR
• Where I = current flowing through the circuit.
• Using equation(1), Vm sinωt = IR
• => I = (Vm/R) sinωt    equation(2)
•  This is the amount of current which flows through the circuit. By substituting  Im  = (Vm/R)  in equation(2)
• Therefore I = Im sinωt
• Where Im = current amplitude or peak value of current. Conclusion:-

If alternating voltage is applied to a circuit which has only a resistor then the current flowing through the circuit will also be alternating current.

This means the current flowing through a circuit is also a sinusoidal function.

Graphical representation of voltage & current

• From the graph it is clear that although both voltage and current are sinusoidal function but the peak value of current is less  than the peak value of voltage. As Im = (Vm/R)  => Im < Vm.
• Voltage and current are in phase with each other which means  both of them reach their maximum value, then 0 and  their minimum value  at the same time.
• Average current  over a complete cycle is zero.
• Average voltage  over a  complete cycle is zero.
• V = Vm sinωt
•  Where V = instantaneous value of voltage at time t.
• I = Im sinωt
• Where I = instantaneous value of current at any time t.

The given graph is showing  that in a pure resistor, the voltage and current are in phase. The minima, zero and maxima occur at the same respective times. .