Question

The incorrect statement for L-R-C series circuit is

• A. The potential difference across the resistance and the appleid e.m.f. are always in same phase
• B. The phase difference across inductive coil is ${90}^0$
• C. The phase difference between the potential difference across capacitor and potential difference across inductance is ${90}^0$
• D. The phase difference between potential difference across capacitor and potential difference across resistance is ${90}^0$

Answer 1

The correct option is C The phase difference between the potential difference across capacitor and potential difference across inductance is ${90}^0$

Solution:-

Here, we have series LCR ckt as

V: Input voltage

$\omega$ = angular frequency of sinusoidal waveform

Now, as we know

Potential drop across inductor is $V_L=I{X}_L$

where I is current flowing through circuit and X_L is Reactance across inductor i.e.

$X_L=j\omega L⟶\left(ii\right)$

Now we know

$\cos \theta +j\sin \theta =e^{j\theta }$4

$\cos \frac{R}{2}+j\sin \frac{\pi }{2}=e^{j\frac{R}{2}}=j$

$j=e^{j\frac{R}{2}}⟶e{q}^n\left(iii\right)$

Using $e{q}^n\left(ii\right)and\left(iii\right);e{q}^n\left(i\right)$ becomes

$V_L=\omega LI{e}^{j\frac{\pi }{2}}$

Hence potential difference across inductor Leaads by phase $\frac{\pi }{2}$.

Similarly, for potential difference across capacitor, we get

$V_C=I{X}_C$

$X_C=-\frac{j}{\omega C}$

$V_C=\frac{1}{\omega C}{e}^{-j\frac{\pi }{2}}$

Hence potential difference across inductor lags by phase $\frac{\pi }{2}$4. And phase diagram will be given as:-

Hence the potential difference across capacitor $\&$ potential difference across inductance is 180 not 90.

Hence option C is INCORRECT STATEMENT.