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In an L-C-R series circuit, the potentia...

In an L-C-R series circuit, the potential difference between the terminals of the inductance is 60 V, between the terminals of the capacitor is 30 V and that across the resistance is 40 V. Then, the supply voltage will be equal to

A

10 V

B

50 V

C

70 V

D

130 V

Text Solution

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The correct Answer is:
To find the supply voltage \( V_s \) in an L-C-R series circuit, we can use the relationship between the voltages across the inductor \( V_L \), capacitor \( V_C \), and resistor \( V_R \). ### Step 1: Identify the given values - Voltage across the inductor \( V_L = 60 \, V \) - Voltage across the capacitor \( V_C = 30 \, V \) - Voltage across the resistor \( V_R = 40 \, V \) ### Step 2: Understand the phasor relationship In an L-C-R series circuit, the voltages across the inductor and capacitor are out of phase by 180 degrees. This means we can treat them as vector quantities where: - \( V_L \) and \( V_C \) will subtract from each other. - \( V_R \) is in phase with the supply voltage \( V_s \). ### Step 3: Calculate the net voltage across the inductor and capacitor The net voltage across the inductor and capacitor can be calculated as: \[ V_{LC} = V_L - V_C = 60 \, V - 30 \, V = 30 \, V \] ### Step 4: Apply the Pythagorean theorem The supply voltage \( V_s \) can be calculated using the Pythagorean theorem, since \( V_R \) is in phase with \( V_s \): \[ V_s = \sqrt{V_{LC}^2 + V_R^2} \] Substituting the values we have: \[ V_s = \sqrt{(30 \, V)^2 + (40 \, V)^2} \] ### Step 5: Calculate the squares Calculating the squares: \[ V_s = \sqrt{900 + 1600} \] ### Step 6: Sum the squares \[ V_s = \sqrt{2500} \] ### Step 7: Take the square root \[ V_s = 50 \, V \] ### Final Answer The supply voltage \( V_s \) is \( 50 \, V \). ---
To find the supply voltage \( V_s \) in an L-C-R series circuit, we can use the relationship between the voltages across the inductor \( V_L \), capacitor \( V_C \), and resistor \( V_R \). ### Step 1: Identify the given values - Voltage across the inductor \( V_L = 60 \, V \) - Voltage across the capacitor \( V_C = 30 \, V \) - Voltage across the resistor \( V_R = 40 \, V \) ### Step 2: Understand the phasor relationship ...
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