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

Options

A. 10 V
B. 50 V
C. 70 V
D. 130 V

Explanation

To find the supply voltage in an L-C-R series circuit, we can use the relationship between the voltages across the components. The total supply voltage \( V \) can be calculated using the formula:

\[ V = \sqrt{V_R^2 + (V_L - V_C)^2} \]

Where:
- \( V_R \) is the voltage across the resistor,
- \( V_L \) is the voltage across the inductor,
- \( V_C \) is the voltage across the capacitor.

Given:
- \( V_L = 60 \, V \) (voltage across the inductor),
- \( V_C = 30 \, V \) (voltage across the capacitor),
- \( V_R = 40 \, V \) (voltage across the resistor).

Now, we can substitute these values into the formula.

### Step 1: Substitute the values into the formula
\[ V = \sqrt{(40)^2 + (60 - 30)^2} \]

### Step 2: Calculate the difference between the inductor and capacitor voltages
\[ V_L - V_C = 60 - 30 = 30 \, V \]

### Step 3: Substitute back into the formula
\[ V = \sqrt{(40)^2 + (30)^2} \]

### Step 4: Calculate the squares
\[ V = \sqrt{1600 + 900} \]

### Step 5: Add the results
\[ V = \sqrt{2500} \]

### Step 6: Take the square root
\[ V = 50 \, V \]

Thus, the supply voltage will be equal to **50 V**.

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