Question:
A step down transformer increases the input current 4 A to 24 A at the secondary. If the number of turns in the primary coil is 330, the number of turns in the secondary coil is
A step down transformer increases the input current 4 A to 24 A at the secondary. If the number of turns in the primary coil is 330, the number of turns in the secondary coil is
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In a step-down transformer, the voltage decreases, which means the current must increase to conserve power (\( P = VI \)). Consequently, the secondary coil always has fewer turns than the primary coil.
Updated On: May 6, 2026
- 60
- 50
- 65
- 45
- 55
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The Correct Option is
Solution and Explanation
Concept:
An ideal transformer operates on the principle of mutual induction, preserving power (ignoring losses).
• Transformer Ratio: The ratio of voltages, turns, and currents is given by: \[ \frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} \]
• Inverse Relationship: Notice that the number of turns is directly proportional to voltage but inversely proportional to current.
Step 1: Set up the ratio between current and turns.
We are given the primary and secondary currents (\( I_p, I_s \)) and the primary turns (\( N_p \)). We need to find the secondary turns (\( N_s \)): \[ \frac{N_s}{N_p} = \frac{I_p}{I_s} \]
Step 2: Solve for \( N_s \).
Substitute the given values: \( I_p = 4 \text{ A} \), \( I_s = 24 \text{ A} \), and \( N_p = 330 \). \[ \frac{N_s}{330} = \frac{4}{24} \] Simplify the fraction: \[ \frac{N_s}{330} = \frac{1}{6} \] \[ N_s = \frac{330}{6} = 55 \]
• Transformer Ratio: The ratio of voltages, turns, and currents is given by: \[ \frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} \]
• Inverse Relationship: Notice that the number of turns is directly proportional to voltage but inversely proportional to current.
Step 1: Set up the ratio between current and turns.
We are given the primary and secondary currents (\( I_p, I_s \)) and the primary turns (\( N_p \)). We need to find the secondary turns (\( N_s \)): \[ \frac{N_s}{N_p} = \frac{I_p}{I_s} \]
Step 2: Solve for \( N_s \).
Substitute the given values: \( I_p = 4 \text{ A} \), \( I_s = 24 \text{ A} \), and \( N_p = 330 \). \[ \frac{N_s}{330} = \frac{4}{24} \] Simplify the fraction: \[ \frac{N_s}{330} = \frac{1}{6} \] \[ N_s = \frac{330}{6} = 55 \]
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