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A high tension wire is at a high potenti...

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.
Consider a bird having effective resistance `10 Omega` between its feet sitting on this high tension wire. The distance between its feet is 10 cm. Find the potential difference between the feet of the bird is approximately,

A

0.1 V

B

1 V

C

10 V

D

0.05 V

Text Solution

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The correct Answer is:
To find the potential difference between the feet of the bird sitting on the high tension wire, we can follow these steps: ### Step 1: Understand the Setup We have a high tension wire carrying a current of 1 A, and the resistance of the wire is given as 1 Ω/m. The bird has a resistance of 10 Ω between its feet, and the distance between its feet is 10 cm (0.1 m). ### Step 2: Calculate the Resistance Between the Feet of the Bird Since the distance between the bird's feet is 10 cm (0.1 m), we can calculate the resistance of the wire segment between the bird's feet: \[ R_{\text{wire}} = \text{Resistance per meter} \times \text{Distance} = 1 \, \Omega/\text{m} \times 0.1 \, \text{m} = 0.1 \, \Omega \] ### Step 3: Set Up the Circuit The bird's feet create a parallel circuit with the resistance of the bird (10 Ω) and the resistance of the wire segment (0.1 Ω). The total current flowing through the high tension wire is 1 A. ### Step 4: Apply the Current Division Rule Let \( I_1 \) be the current through the bird's resistance (10 Ω) and \( I_2 \) be the current through the wire segment (0.1 Ω). According to the junction rule: \[ I_1 + I_2 = 1 \, \text{A} \] The potential difference across both resistors is the same, so we can write: \[ V = I_1 \times 10 = I_2 \times 0.1 \] ### Step 5: Express \( I_2 \) in Terms of \( I_1 \) From the potential difference equation: \[ I_2 = \frac{10}{0.1} I_1 = 100 I_1 \] ### Step 6: Substitute \( I_2 \) into the Current Equation Substituting \( I_2 \) into the current equation gives: \[ I_1 + 100 I_1 = 1 \] \[ 101 I_1 = 1 \] \[ I_1 = \frac{1}{101} \, \text{A} \] ### Step 7: Calculate the Potential Difference Now we can calculate the potential difference \( V \) across the bird's feet: \[ V = I_1 \times 10 = \frac{1}{101} \times 10 \approx 0.099 \, \text{V} \approx 0.1 \, \text{V} \] ### Conclusion The potential difference between the feet of the bird is approximately **0.1 V**. ---
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