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 potential difference between H.T and earth wire is 11 kV at point A, find p.d between these wires at point B

Options

A. 1 KV
B. 2 KV
C. 9 KV
D. 10 KV

Answer

To solve the problem, we need to find the potential difference between the high tension (HT) wire and the earth wire at point B, given that the potential difference at point A is 11 kV.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Distance between points A and B = 1 km = 1000 m
- Distance between HT wire and earth wire = 1 m
- Resistance of HT wire = 1 Ω/m
- Resistance of earth wire = 1 Ω/m
- Potential at point A (VA) = 11 kV = 11,000 V
- Current (I) = 1 A

2. **Calculate the Total Resistance:**
- The length of the HT wire from A to B is 1000 m, so the resistance of the HT wire (R_HT) is:
\[ R_{HT} = 1 \, \Omega/m \times 1000 \, m = 1000 \, \Omega \]
- The length of the earth wire from A to B is also 1000 m, so the resistance of the earth wire (R_EW) is:
\[ R_{EW} = 1 \, \Omega/m \times 1000 \, m = 1000 \, \Omega \]

3. **Determine the Potential Drop Across the HT Wire:**
- The potential drop (V_drop) across the HT wire can be calculated using Ohm's law:
\[ V_{drop} = I \times R_{HT} = 1 \, A \times 1000 \, \Omega = 1000 \, V \]

4. **Calculate the Potential at Point B (VB):**
- The potential at point B (VB) can be calculated as:
\[ V_A - V_B = V_{drop} \]
\[ 11,000 \, V - V_B = 1000 \, V \]
\[ V_B = 11,000 \, V - 1000 \, V = 10,000 \, V = 10 \, kV \]

5. **Determine the Potential at the Earth Wire at Point B (VB'):**
- The potential at the earth wire at point B (VB') is:
\[ V_{B'} = 0 \, V \quad \text{(since it's grounded)} \]

6. **Calculate the Potential Difference Between the HT Wire and Earth Wire at Point B:**
- The potential difference (PD) between the HT wire and the earth wire at point B is:
\[ PD = V_B - V_{B'} = 10,000 \, V - 0 \, V = 10,000 \, V = 10 \, kV \]

### Final Answer:
The potential difference between the high tension wire and the earth wire at point B is **10 kV**.

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