Using the equation of power for an ideal transformer,prove $\frac{I_p}{I_s} = \frac{V_s}{V_p} = \frac{N_s}{N_p}$.

The coils of a step-down transformer have $500$ and $5000$ turns. In the primary coil, an $AC$ current of $4 \,A$ at $2200 \,V$ is sent. The value of the current and potential difference in the secondary coil is:

The instrument which works on the principle of mutual inductance is

$A$ 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 $2$.

The turn ratio of a transformer is given as $2 : 3$. If the current through the primary coil is $3 \, A$,calculate the current through the load resistance (secondary coil). (in $, A$)

$A$ current of $5 \,A$ is flowing at $220 \,V$ in the primary coil of a transformer. If the voltage produced in the secondary coil is $2200 \,V$ and $50 \%$ of power is lost, then the current in the secondary will be (in $A$)