  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 900  C
The phase difference between the potential difference across capacitor and potential difference across inductance is 900  D
The phase difference between potential difference across capacitor and potential difference across resistance is 900  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 asV: Input voltage$$\omega$$  = angular frequency of sinusoidal waveformNow, 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}} = jj = 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_CX_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. Physics

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