Ncert Exercises & Solutions

1 MW power is to be delivered from a power station to a town 10 Km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose.
Calculate the fraction of ohmic losses to the power transmitted if;

(i) power is transmitted at 220V. Comment on the feasibility of doing this.

(ii) a step-up transformer is used to boost the voltage to 11000V, power transmitted, then a step-down transformer is used to bring a voltage to 220 V. $(ρ_{c u} = 1.7 \times 10^{- 8} S I u n i t)$

Hint: The power losses depend on the current flowing in the wires.

(i) Step 1: The town is 10 km away, length of pair of Cu wires used, L=20 km=20000 m.

Resistane of Cu wires, R = ρ \frac{l}{A} = ρ \frac{l}{π {(r)}^{2}}

= \frac{1.7 \times 10^{- 8} \times 20000}{3.14 \times {(0.5 \times 10^{- 2})}^{2}} = 4 Ω

At 220 V, VI = 10^{6} W; I = \frac{10^{6}}{220} = 0.45 \times 10^{4} A

Power loss = {RI}^{2}

= 4 \times {(0.45)}^{2} \times 10^{8} W

> 10^{6} W

Therefore, this method cannot be used for transmission.

Step 2:

(ii) When power P = 10^{6} W is transmitted at 11000 V,

V' I' = 10^{6} W = 11000 I'

Current drawn, I' = \frac{1}{1.1} \times 10^{2}

Power loss = {RI}^{2} = \frac{1}{1.21} \times 4 \times 10^{4}

= 3.3 \times 10^{4} W

Fraction of power loss = \frac{3.3 \times 10^{4}}{10^{6}} = 3.3 %

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