Question

When an alternating voltage of `220 V` is applied across a device `P`, a current of `0.25 A` flows through the circuit and it leads the applied voltage by a angle `pi/2` radian. When the same voltage source is connected across another device `Q`, the same current is observed in the circuit but in phase with the applied voltage. What is the current when the same source is connected across a series combination of `P` and `Q`?
A. `1/(4sqrt2)` A lagging in phase by `pi/4` with voltage
B. `1/(4sqrt2)` A leading in phase by `pi/4` with voltage
C. `1/sqrt2` A leading in phase by `pi/4` with voltage
D. `1/(4sqrt2)` A leading in phase in `pi/2` with voltage

Answer 1

Correct Answer - B
In the first case `X_C=V/I=220/0.25=880Omega`
In the second case, `R=V/I=225/0.25=880Omega`
In the comgination of `P` and `Q`.
`tanphi=X_C/R=1`
`:. phi=4^@`
since the circuit is capacitive current leads the voltage. Further,
`Z=sqrt(R^2+X_C^2)=880sqrt2Omega`
`I=V/Z=220/(880sqrt2)=1/(4sqrt2)A`.