Question

In an LCR series ac circuit the voltage across each of the components \(\mathrm{L}, \mathrm{C}\) and \(\mathrm{R}\) is \(50 \mathrm{~V}\). The voltage across the LC combination will be (a) \(50 \mathrm{~V}\) (b) \(50 \sqrt{2} \mathrm{~V}\) (c) \(100 \mathrm{~V}\) (d) \(0 \mathrm{~V}\) (zero)

Short answer

The voltage across the LC combination in an LCR series AC circuit with voltages of 50 V across L, C, and R components is 0 V (zero), as the voltages across the inductor (L) and capacitor (C) are out of phase by 180 degrees and cancel each other out when added using phasor addition. The correct answer is (d) \(0 \mathrm{~V}\) (zero).

Step-by-step solution

Identify the Voltages Across Components

The voltage across each of the components is given as 50 V. So, we have: \(V_L = 50 V\) \(V_C = 50 V\) Now, we will find the voltage across the LC combination (V_LC) using phasor addition.

Phasor Addition

In an LCR series AC circuit, the voltages across the inductor (L) and capacitor (C) are out of phase by 180 degrees. To find the resultant voltage across the LC combination, we need to add the voltages of L and C using phasor addition, considering their phase difference. Since they are out of phase by 180 degrees, the total voltage across LC is given by: \(V_{LC} = |V_L - V_C|\)

Calculating Voltage Across LC Combination

Now, we can plug in the values for V_L and V_C and calculate the voltage across the LC combination: \( V_{LC} = |50 V - 50 V|\) \(V_{LC} = |0 V|\) \(V_{LC} = 0 V\) So, the voltage across the LC combination will be 0V (zero). The correct answer is: (d) \(0 \mathrm{~V}\) (zero)