In a transformer,the mutual inductance between the primary and secondary coils is $0.5 \ H$. The resistances of the primary and secondary coils are $20 \ \Omega$ and $5 \ \Omega$ respectively. To induce a current of $0.4 \ A$ in the secondary coil,what is the required rate of change of current in the primary coil in $A/s$?

Which of the following statements is correct regarding a step-down transformer?

$A$ transformer is a device which converts

$A$ transformer has a turn ratio of $100/1$. If the secondary coil has a $4 \, A$ current,then the current in the primary coil is......$A$

$A$ transformer having an efficiency of $90 \%$ is working on a $200 \ V$ and $3 \ kW$ power supply. If the current in the secondary coil is $6 \ A$,the voltage across the secondary coil and the current in the primary coil respectively are:

$A$ small town with a demand of $800 \; kW$ of electric power at $220 \; V$ is situated $15 \; km$ away from an electric plant generating power at $440 \; V$. The resistance of the two-wire line carrying power is $0.5 \; \Omega/km$. The town gets power from the line through a $4000-220 \; V$ step-down transformer at a sub-station in the town.
$(a)$ Estimate the line power loss in the form of heat.
$(b)$ How much power must the plant supply,assuming there is negligible power loss due to leakage?
$(c)$ Characterise the step-up transformer at the plant.