Question

A transformer is connected to a 200 V ac source. The transformer supplies 3000 V to a device. If the number of turns in the primary coil is 450, then the number of turns in its secondary coil is

• A. 30
• B. 450
• C. 4500
• D. 6750

Hint:

Use \(N_s/N_p = V_s/V_p\).

Answer 1

The Correct Option is D

Step 1: Recall the transformer relation:
For an ideal transformer, the ratio of the output (secondary) voltage to the input (primary) voltage equals the ratio of the number of turns.
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \]

Step 2: Substitute:
Here \(V_p = 200\) V, \(V_s = 3000\) V and \(N_p = 450\).
\[ N_s = N_p \times \frac{V_s}{V_p} = 450 \times \frac{3000}{200} = 450 \times 15 = 6750 \]

Step 3: Check the options:
The voltage rises by a factor of 15, so it is a step up transformer and the secondary must have more turns than the primary.
(A) 30 and (B) 450 would not step up the voltage by 15 (30 gives a step down; 450 gives no change).
(C) 4500 would give only 10 times the voltage, that is 2000 V.
(D) 6750 gives exactly 3000 V, so it is correct.

Final Answer:
The secondary coil has 6750 turns, option (D). \[ \boxed{N_s = 6750} \]