An a.c. circuit has a chock coil L and resistance R. The potential difference across the chocke is `v_(L) = 160 V` and that across the resistance `v_(R) = 120V`. Find the virtual value of the applied voltage. If the virtual current in the circuit be 1.0 A, then calculate the total impedance of the circuit. If a direct current be passed in the circuit, then what will be the potential difference in the circuit ?

Answer

To solve the problem step by step, we will follow the outlined requirements.

### Step 1: Calculate the virtual value of the applied voltage (V_rms)

The total voltage across the circuit in an AC circuit with a choke coil (inductor) and a resistor can be calculated using the formula:

\[ V_{rms} = \sqrt{V_L^2 + V_R^2} \]

Where:
- \( V_L = 160 \, V \) (potential difference across the choke coil)
- \( V_R = 120 \, V \) (potential difference across the resistance)

Substituting the values:

\[ V_{rms} = \sqrt{(160)^2 + (120)^2} \]
\[ = \sqrt{25600 + 14400} \]
\[ = \sqrt{40000} \]
\[ = 200 \, V \]

### Step 2: Calculate the total impedance of the circuit (Z)

We know the virtual current in the circuit is given as \( I = 1 \, A \). The impedance can be calculated using Ohm's law for AC circuits:

\[ Z = \frac{V_{rms}}{I} \]

Substituting the values:

\[ Z = \frac{200 \, V}{1 \, A} = 200 \, \Omega \]

### Step 3: Calculate the potential difference in the circuit when a direct current is passed

When a direct current (DC) is passed through the circuit, the inductor behaves like a short circuit (a simple wire). Therefore, the potential difference across the circuit will be equal to the potential difference across the resistor:

\[ V = V_R = 120 \, V \]

### Final Answers:
1. The virtual value of the applied voltage \( V_{rms} = 200 \, V \).
2. The total impedance of the circuit \( Z = 200 \, \Omega \).
3. The potential difference in the circuit with DC \( V = 120 \, V \).

---