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A resistor of $$200$$ohm and capacitance $$15$$ micro farad are connected in series to a $$220$$V and $$50$$Hz source. Calculate the voltage rms across the resistor and capacitor is the algebraic sum of these voltage more than the source voltage ? if yes, resolve the paradox
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## QuestionPhysicsClass 12

A resistor of $$200$$ohm and capacitance $$15$$ micro farad are connected in series to a $$220$$V and $$50$$Hz source. Calculate the voltage rms across the resistor and capacitor is the algebraic sum of these voltage more than the source voltage ? if yes, resolve the paradox

Since the current is the same through the circuit. We have
$$v_R=\mathit{IR}=0.755\times 200=151V$$
$$V_C=IX_c=0755\times 212.3=160.3$$ V
The algebraic sum of the two voltages. $$V$$ and   $$V_C$$  is $$311.3V$$  which is more than the source voltage of $$220V$$ . How to resolve this paradox?
As you have learnt in the text, The two voltages are not in the same phase. Therefore. they cannot be added like ordinary numbers. The two voltages are out of phase by ninety degrees. Therefore, the total of these voltages must be obtained using the Pythagorean theorem:
$$V_{RC}=\sqrt{V_R^2+V_C^2}$$
$$220V$$
Thus, if the phase difference between two voltages is properly taken Into account, the total voltage across the resistor and the capacitor is equal to the voltage of the source.