In a step up transformer, the voltage in the primary is \(220\text{ V}\) and the current is \(5\text{ A}\). The secondary voltage is found to be \(22000\text{ V}\). The current in the secondary coil (neglect losses) is:
In an ideal transformer, input power equals output power: \(V_p I_p = V_s I_s\). Therefore, \(I_s = \frac{V_p I_p}{V_s} = \frac{220 \times 5}{22000} = 0.05\text{ A}\).
A step down transformer connected to an ac mains supply of \(220\text{ V}\) is made to operate at \(11\text{ V}\), \(44\text{ W}\) lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?
Assuming zero power losses, the input power in the primary circuit equals the output power in the secondary circuit: \(P_{\text{in}} = P_{\text{out}} = 44\text{ W}\). Since \(P_{\text{in}} = V_p I_p\), we get \(I_p = \frac{P_{\text{in}}}{V_p} = \frac{44}{220} = 0.2\text{ A}\).
In an ideal transformer, the turns ratio is \(\frac{N_p}{N_s} = \frac{1}{3}\). The ratio of \(I_s : I_p\) is equal to (symbols carry their usual meaning):
For an ideal transformer, input power equals output power: \(V_p I_p = V_s I_s ⇒ \frac{I_s}{I_p} = \frac{V_p}{V_s} = \frac{N_p}{N_s} = \frac{1}{3}\).
The ratio of secondary to primary turns in a transformer is 4 : 1. If the power input is P, then output power neglecting all losses must be equal to
In an ideal transformer, there is no energy loss. Therefore, the output power is equal to the input power, which is P.
Assertion (A): A transformer cannot work on D.C. supply.
Reason (R): D.C. changes neither in magnitude nor in direction.
Transformers rely on mutual induction, which requires a changing magnetic flux. DC current, being constant (R), produces a steady flux, thus no induced EMF. Both A and R are true, and R correctly explains A.
Assertion (A): If we use a battery across the primary of a step up transformer, no voltage is obtained across secondary.
Reason (R): Battery gives a steady current.
Assertion (A) is true. Transformers require a changing magnetic flux to induce voltage. Reason (R) is true; a battery provides DC current. This steady current causes constant flux, hence no induced emf in the secondary. (R) correctly explains (A).