Question 9: In an RC series circuit, will the current lag or lead the applied alternating voltage? Explain the answer with a phasor diagram.

### RC series circuit

RC series circuit is one which consists of a pure resistance R and a pure capacitance C connected in series with an alternating (sinusoidal) voltage source.

### Analysis of RC series circuit

Consider a circuit consisting of a resistance R and capacitance C connected in series with an AC source.

We see that

1. The potential drop VR across the resistance R is in phase with the current I. So

Here I and VR are the instantaneous values of current and potential drop across resistance R and ω is the angular velocity of the AC source. The phasor is as below.

2. Potential drop VC across the capacitance C lags behind the current I by π/2 rad. So if,

The phasor diagram is shown below.

Here the same current passes through R and C. Now the voltage drop VR = IR is in phase with the current. Similarly, voltage drop VC lags behind the current by 900. Therefore, the phasor diagram of the applied voltage V is the vector sum of the V ⃑_R andV ⃑_C.

From the figure, it is clear that it is still lagging behind the current. However, the phase angle φ is less than 900. So the phase difference between current and voltage is between 00 and 900.

Thus in the RC series circuit, the current leads the applied voltage. This is illustrated in the wave diagram as below.

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