Question

Obtain an expression for the current flowing in a circuit containing resistance only to which alternating emf is applied. Explain the phase relationship between voltage and current with a graph.

Answer 1

Let an alternating source of emf is connected across a resistor of resistance $R$.
The instantaneous value of the applied emf is $e=E_0\sin \omega t$ ....(1)
If $i$ is the current through the circuit at the instant $t$, the potential drop across $R$ is, $e=iR$.
Potential drop must be equal to the applied emf.
Hence, $iR=E_0\sin \omega t$
$i=\frac{E_0}{R}\sin \omega t$; $i=I_0\sin \omega t$ .....(2)
where $I_0=\frac{E_0}{R}$, is the peak value of a.c. in the circuit.
Equation (2) gives the instantaneous value of current in the circuit containing $R$. From the expressions of voltage and current given by equations (1) and (2) it is evident that in a resistive circuit, the applied voltage and current are in phase with each other figure (b).
Figure (c) is the phasor diagram representing the phase relationship between the current and the voltage.