Question

The output of a generator is 440 V at 20 A. It is to be transmitted on a line with resistance of 0.60 Ω. To what voltage must the generator output be stepped up with a transformer if the power loss in transmission is not to exceed 0.010% of the original power?

Answer 1

Answer:

The voltage of the generator is 7.27 kV.

Explanation:

Given that,

Output of generator = 440 V

Current = 20 A

Resistance = 0.60 Ω

Power loss =0.010%

We need to calculate the total power of the generator

Using formula of power

$P=VI$

Where, V = voltage

I = current

Put the value into the formula

$P=440\times20$

$P=8800\ W$

Th power lost on the transmission lines

$P_{L}=0.010\% P$

$P_{L} = 0.010\%\times8800$

$P_{L}=0.88\ W$

The current passing through the transmission line

$I'=\sqrt{\dfrac{P_{L}}{R}}$

$I'=\sqrt{\dfrac{0.88}{0.60}}$

$I'=1.211\ A$

We need to calculate the voltage of the generator

Using formula of voltage

$V_{g}=\dfrac{P}{I'}$

Put the value into the formula

$V_{g}=\dfrac{8800}{1.211}$

$V_{g}=7.27\times10^{3}\ V$

$V_{g}=7.27\ kV$

Hence, The voltage of the generator is 7.27 kV.