Question

Three ac circuits are shown in the figures with equal currents. Explain with reason, if the frequency of the voltage \( E \) is increased then what will be the effect on the currents in them.
\includegraphics[width=0.5\linewidth]{image4.png}

Hint:

The behavior of current in an AC circuit depends on the type of element present. In resistive circuits, current is unaffected by frequency; in inductive circuits, current decreases with increasing frequency; and in capacitive circuits, current increases with increasing frequency.

Answer 1

The three types of circuits given are:
1. A resistive circuit (\( R \)),
2. An inductive circuit (\( L \)),
3. A capacitive circuit (\( C \)). Resistive Circuit: In a purely resistive circuit, the current \( I \) is related to the applied voltage \( V \) by Ohm's law:
\[ I = \frac{V}{R} \] Where:
- \( V \) is the voltage across the resistor,
- \( R \) is the resistance.
In a resistive circuit, the current is independent of frequency. Therefore, increasing the frequency of the voltage will not affect the current in a purely resistive circuit.
Inductive Circuit: In a purely inductive circuit, the current \( I \) lags the voltage by \( 90^\circ \), and the impedance \( Z_L \) is given by:
\[ Z_L = \omega L = 2 \pi f L \] Where:
- \( \omega \) is the angular frequency (\( \omega = 2 \pi f \)),
- \( L \) is the inductance,
- \( f \) is the frequency of the voltage.
As the frequency increases, the inductive reactance \( X_L \) increases, which causes the impedance \( Z_L \) to increase. According to Ohm's law for AC circuits, the current decreases as the impedance increases. Therefore, increasing the frequency decreases the current in an inductive circuit.
Capacitive Circuit: In a purely capacitive circuit, the current \( I \) leads the voltage by \( 90^\circ \), and the impedance \( Z_C \) is given by:
\[ Z_C = \frac{1}{\omega C} = \frac{1}{2 \pi f C} \] Where:
- \( C \) is the capacitance,
- \( f \) is the frequency of the voltage.
As the frequency increases, the capacitive reactance \( X_C \) decreases, which causes the impedance \( Z_C \) to decrease. According to Ohm's law, as the impedance decreases, the current increases. Therefore, increasing the frequency increases the current in a capacitive circuit.
Thus, the effect of increasing frequency on the current in the three circuits is:
- In the resistive circuit, the current remains unchanged.
- In the inductive circuit, the current decreases.
- In the capacitive circuit, the current increases.