$A$ loss-free transformer has $500$ turns on its primary winding and $2500$ turns in its secondary winding. The meters of the secondary indicate $200 \, V$ at $8 \, A$ under these conditions. The voltage and current in the primary are:

In an ideal transformer,the turns ratio is $\frac{N_p}{N_S} = \frac{1}{2}$. The ratio $V_s : V_p$ is equal to (the symbols carry their usual meaning):

Which device is used to transmit voltage over large distances and why?

$A$ thermal power plant produces electric power of $600 \ kW$ at $4000 \ V$,which is to be transported to a place $20 \ km$ away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers,the dissipation is much smaller. In this method,a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end,a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with a power factor unity. All the currents and voltages mentioned are rms values.
$1.$ If the direct transmission method with a cable of resistance $0.4 \ \Omega \ km^{-1}$ is used,the power dissipation (in %) during transmission is:
$(A) 20$ $(B) 30$ $(C) 40$ $(D) 50$
$2.$ In the method using the transformers,assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is $1:10$. If the power to the consumers has to be supplied at $200 \ V$,the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is:
$(A) 200:1$ $(B) 150:1$ $(C) 100:1$ $(D) 50:1$
Give the answer for question $1$ and $2$.

Write important uses of transformer.

In an ideal step-up transformer,if the input voltage and input power are $V_1$ and $P_1$ respectively,and the output voltage and output power are $V_2$ and $P_2$ respectively,then