When an alternating voltage of 220v is applied across a device x a cur...
Device X:
When an alternating voltage of 220V is applied across device X, a current of 0.5A flows through the circuit. The current flowing through device X is in phase with the applied voltage.
Device Y:
When the same voltage of 220V is applied across device Y, the same current of 0.5A flows through the circuit. However, the current flowing through device Y leads the applied voltage by π/2 radians or 90 degrees.
Current in the Circuit:
When the same voltage is applied across the series combination of device X and device Y, we can calculate the total current flowing in the circuit.
Explanation:
To calculate the total current, we need to consider the impedance of the devices X and Y. Impedance is a measure of opposition to the flow of alternating current in a circuit and is represented by the symbol Z.
Impedance of Device X:
Since the current in device X is in phase with the applied voltage, it means that the impedance of device X is purely resistive. Let's represent the impedance of device X as RX.
Impedance of Device Y:
Since the current in device Y leads the applied voltage by π/2 radians, it means that the impedance of device Y has both a resistive and reactive component. Let's represent the impedance of device Y as RY + jXY, where j represents the imaginary unit and XY represents the reactive component.
Total Impedance:
The total impedance is the sum of the individual impedances. Therefore, the total impedance of the series combination of device X and device Y is Z = RX + RY + jXY.
Current Calculation:
Using Ohm's Law, we can calculate the total current flowing in the circuit by dividing the applied voltage by the total impedance.
I = V/Z
Substituting the values, we have:
I = 220V / (RX + RY + jXY)
Since the current in the circuit is the same as the current flowing through device X and device Y, the calculated current will be the same 0.5A.
Conclusion:
In summary, device X has a purely resistive impedance, while device Y has both a resistive and reactive component. When the same voltage is applied across the series combination of device X and device Y, the total current flowing in the circuit remains the same as the individual currents in device X and device Y.