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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
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B
The phase difference across inductive coil is 900
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C
The phase difference between the potential difference across capacitor and potential difference across inductance is 900
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D
The phase difference between potential difference across capacitor and potential difference across resistance is 900
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Solution

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 $$V_L = IX_L$$ 

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

$$X_L = j\omega L \longrightarrow \left(ii\right)$$

 Now we know

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

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

$$j = e^{j\cfrac{R}{2}} \longrightarrow eq^n \left(iii\right)$$

Using $$eq^n \left(ii\right) and \left(iii\right); eq^n \left(i\right)$$ becomes

$$V_L = \omega LIe^{j\cfrac{\pi}{2}}$$


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

Similarly, for potential difference across capacitor, we get

$$V_C = IX_C$$

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

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

Hence potential difference across inductor lags by phase $$\cfrac{\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.


858874_22566_ans_f4ada874051a4aad8c04d4736f6bbdf7.png

Physics

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