Question

In a transformer, the number of turns of the primary coil and secondary coil are 5 and 4 respectively. If 220V is applied on the primary coil, then the ratio of primary current to the secondary current is
A) 4:5
B) 5:4
C) 5:9
D) 9:5

Answer 1

Hint: A transformer is usually used to change the voltage of alternating current. The Ratio of the EMFs in the primary and the secondary coil is equal to the ratio of the number of coils in the primary to the secondary coil.

Formula Used: In this solution we will be using the following formula,
 $ \dfrac{{{V_1}}}{{{V_2}}} = \dfrac{{{n_1}}}{{{n_2}}} $ where $ {V_1},{V_2} $ are the voltages in the primary and secondary coils and $ {n_1},{n_2} $ are the number of turns on the primary and secondary coils.

Complete step by step answer:
In a transformer, the voltage of the alternating current can be stepped up or down by using a different number of coils in the primary and the secondary circuit. A step-up transformer changes the voltage into higher voltage while a step-down transformer lowers the voltage of the alternating current while keeping the power transferred as constant.
So, we can write that
 $ \dfrac{{{V_1}}}{{{V_2}}} = \dfrac{{{n_1}}}{{{n_2}}} $
Substituting the value of $ {V_1} = 220,\,{n_1} = 5\,{\text{and}}\,{{\text{n}}_2} = 4 $ , we get
 $ \dfrac{{220}}{{{V_2}}} = \dfrac{5}{4} $
 $ \Rightarrow {V_2} = 176\,V $
Since the number of turns in the secondary coil is lesser than the number of turns in the primary coil, the voltage in the secondary loop is lower so this is a step-down transformer. Since the power transferred in a transformer is constant, from the relation $ P = VI $ where $ P $ is the power transferred and $ I $ is the current, we can write
 $ {V_1}{I_1} = {V_2}{I_2} $
Hence we get the ratio as,
 $ \dfrac{{{I_1}}}{{{I_2}}} = \dfrac{{{V_2}}}{{{V_1}}} = \dfrac{{{n_2}}}{{{n_1}}} $
 $ \therefore \dfrac{{{I_1}}}{{{I_2}}} = \dfrac{4}{5} $

Hence, the ratio of the current in the primary to the secondary coil is 4:5 so the correct choice is option (A).

Note: The ratio of currents in the primary to the secondary coil can also be remembered as the inverse of the ratio of voltages and hence the ratio of the number of turns in the secondary to the primary coil which corresponds to 4:5. Here we have assumed that the power transferred across the transformer is complete, that is, there is no energy loss in the transformer while in reality there is always some energy loss which implies that the product of current and voltage in the primary and secondary coil won’t exactly be the same.