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Difficulty: EasyInductors and Transformers

A power supply circuit utilizes a step-down transformer to convert an alternating current (AC) input of 100 V100\text{ V} to an output of 25 V25\text{ V}. If the primary winding contains 400 turns400\text{ turns}, how many turns are on the secondary winding?

  1. A
    1600 turns1{}600\text{ turns}
  2. 100 turns100\text{ turns}Answer
  3. C
    25 turns25\text{ turns}
  4. D
    10 turns10\text{ turns}

Answer

100 turns100\text{ turns}
The correct answer is 100 turns100\text{ turns}. According to the transformer turns ratio law, the ratio of secondary voltage to primary voltage equals the ratio of secondary turns to primary turns: VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}. Rearranging to solve for the secondary turns yields Ns=Np×(VsVp)=400×(25100)=100 turnsN_s = N_p \times \left(\frac{V_s}{V_p}\right) = 400 \times \left(\frac{25}{100}\right) = 100\text{ turns}. Since this is a step-down transformer (100 V100\text{ V} down to 25 V25\text{ V}, a 4:14:1 step-down ratio), the secondary coil must have one-fourth the number of turns of the primary coil.

Step-by-Step Solution

1
Identify the given transformer parameters
Primary voltage Vp=100 VV_p = 100\text{ V}, secondary voltage Vs=25 VV_s = 25\text{ V}, primary turns Np=400 turnsN_p = 400\text{ turns}
Extracting the known values is necessary to set up the turns ratio equation.
2
State the transformer voltage and turns ratio formula
VpVs=NpNs  ⟹  Ns=Np×(VsVp)\frac{V_p}{V_s} = \frac{N_p}{N_s} \implies N_s = N_p \times \left(\frac{V_s}{V_p}\right)
In an ideal transformer, the voltage across each winding is directly proportional to the number of turns.
3
Substitute the values and calculate the secondary winding turns
Ns=400×(25 V100 V)=400×0.25=100 turnsN_s = 400 \times \left(\frac{25\text{ V}}{100\text{ V}}\right) = 400 \times 0.25 = 100\text{ turns}
Performing the proportional calculation gives the exact number of secondary turns required.

Key Concept

Transformer Turns Ratio and Voltage Transformation
Estimated Time:45s
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Topics

Inductors and Transformers

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