Question

A pure resistive circuit element $x$ when connected to an A.C. supply of peak voltage 100 V gives a peak current of 4 A which is in phase with the voltage. A second circuit element y when connected to the same AC supply also gives the same value of peak current but the current lags behind by ${90}^0$. If the series combination of $x$ and $y$ is connected to the same supply, rms value of current is_________

• A. $\frac{5}{\sqrt{2}}A$
• B. $2A$
• C. $\frac{1}{2}$ A
• D. $\frac{\sqrt{2}}{5}A$

Answer 1

Answer: (B)

$2A$

For x : $V_o=100V,I_o=4A,$

Current and Voltage are in phase $\therefore$ circuit is resistive.

now for y, $V_o=100V,I_o=4A$

but current lags by ${90}^{\circ }$ i.e. circuit is inductive

$\frac{100}{4}=X_R=X_L=25\Omega$

now the combination of x and y

$z=\sqrt{{25}^2+{25}^2}$

$=25\sqrt{2}\Omega$

peak $I=\frac{200}{25\sqrt{2}}=2\sqrt{2}A$

$Irms=\frac{2\sqrt{2}}{\sqrt{2}}=2A$