A high tension wire is at a high potential with respect to a wire which is well grounded called Earth wire. You must have seen such wires stretched parallel to roads. There is a high tension wire between two points A and B. 1 km apart. The distance between HT wire and earth wire is 1 m. The resisatnce of the HT (and also the earth wire) is `1 Omega//m`. This wire is at a potential of 11 KV at point A w.r.t. to earth wire. and its is carrying 1 A current which returns back to the generator by through the earth wire. This wire is quite a thick wire. There is a sign board at a pole over which this wire is stretched reading DANGER, 11 KV. You might thick what would happen if one touched this wire. Will one feel a shock or not. Well ! it depends on whether the current through our body exceeds a particular valuem which we may call CRITICAL CURRENT.
If the above question find the current through the bird.

Options

A. `10 A`
B. `1 A`
C. `0.01 A`
D. `0.005 A`

Answer

To find the current through the bird sitting on the high tension wire, we can follow these steps:

### Step 1: Understand the Circuit Configuration
We have a high tension wire (HT wire) and an earth wire. The HT wire is at a potential of 11 kV with respect to the earth wire, and it carries a current of 1 A. The bird is sitting on the HT wire, and the distance between its feet is 0.1 m (10 cm). The resistance of the bird is given as 10 ohms.

### Step 2: Calculate the Resistance of the HT Wire Segment
The resistance of the HT wire is given as 1 ohm/m. Since the distance between the bird's feet is 0.1 m, we can calculate the resistance of this segment of the HT wire:
\[ R_{\text{HT}} = 1 \, \Omega/\text{m} \times 0.1 \, \text{m} = 0.1 \, \Omega \]

### Step 3: Set Up the Current Division
Let \( I_1 \) be the current through the bird and \( I_2 \) be the current through the HT wire. The total current flowing into the junction is 1 A:
\[ I_1 + I_2 = 1 \quad \text{(1)} \]

### Step 4: Apply Ohm's Law to Find the Voltage Drop
The potential difference across the bird can be expressed using Ohm's law:
\[ V = I_1 \times R_{\text{bird}} = I_1 \times 10 \, \Omega \]
The potential difference across the segment of the HT wire is:
\[ V = I_2 \times R_{\text{HT}} = I_2 \times 0.1 \, \Omega \]

Since both resistances are in parallel, the potential difference across them is the same:
\[ 10 I_1 = 0.1 I_2 \quad \text{(2)} \]

### Step 5: Solve the Equations
From equation (2), we can express \( I_2 \) in terms of \( I_1 \):
\[ I_2 = 100 I_1 \]

Now substitute \( I_2 \) into equation (1):
\[ I_1 + 100 I_1 = 1 \]
\[ 101 I_1 = 1 \]
\[ I_1 = \frac{1}{101} \approx 0.0099 \, \text{A} \approx 0.01 \, \text{A} \]

### Conclusion
The current through the bird is approximately \( 0.01 \, \text{A} \).

---