A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit ?

We are given a step‑down transformer whose secondary supplies a lamp that is rated at 11 V and 44 W. The transformer is ideal, so the electrical power transferred from the primary to the secondary is the same.

The secondary power is

$I\_\{secondary\}=\; \backslash frac\{P\_\{secondary\}\}\{V\_\{secondary\}\}\; =\; \backslash frac\{44\backslash \; \backslash text\{W\}\}\{11\backslash \; \backslash text\{V\}\}\; =\; 4\backslash \; \backslash text\{A\}$

However, to find the primary current we do not need the secondary current. Since the transformer is loss‑free, the input power equals the output power:

$P\_\{primary\}=P\_\{secondary\}=44\backslash \; \backslash text\{W\}$

The primary voltage is the mains voltage, 220 V. The primary current therefore follows from

$I\_\{primary\}=\; \backslash frac\{P\_\{primary\}\}\{V\_\{primary\}\}\; =\; \backslash frac\{44\backslash \; \backslash text\{W\}\}\{220\backslash \; \backslash text\{V\}\}\; =\; 0.2\backslash \; \backslash text\{A\}$

Thus the current flowing in the primary circuit of the transformer is 0.2 A.