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Difficulty: HardInductors and Transformers

A step-up transformer in a specialized power supply is connected to a 120 V AC120\text{ V AC} source on its primary side. The secondary circuit delivers a current of 24 mA24\text{ mA} across a 25 kΩ25\text{ k}\Omega resistive load. If the primary winding has 150 turns150\text{ turns}, what is the total number of turns on the secondary winding?

  1. A
    30 turns30\text{ turns}
  2. B
    75 turns75\text{ turns}
  3. 750 turns750\text{ turns}Answer
  4. D
    18 turns18\text{ turns}

Answer

750 turns750\text{ turns}
The correct answer is 750 turns750\text{ turns}. First, determine the secondary voltage using Ohm's Law: Vs=Is×RL=(0.024 A)×(25000 Ω)=600 VV_s = I_s \times R_L = (0.024\text{ A}) \times (25{}000\,\Omega) = 600\text{ V}. Then, apply the transformer ratio formula NsNp=VsVp\frac{N_s}{N_p} = \frac{V_s}{V_p}, yielding Ns=150×(600120)=750 turnsN_s = 150 \times \left(\frac{600}{120}\right) = 750\text{ turns}.

Step-by-Step Solution

1
Calculate the secondary voltage (VsV_s) across the load resistor using Ohm's Law (V=I×RV = I \times R).
Vs=(24 mA)×(25 kΩ)=(0.024 A)×(25000 Ω)=600 VV_s = (24\text{ mA}) \times (25\text{ k}\Omega) = (0.024\text{ A}) \times (25{}000\,\Omega) = 600\text{ V}
Determining the voltage across the secondary winding is necessary to establish the transformer's voltage transformation ratio.
2
Apply the transformer turns ratio equation that relates winding turns directly to voltage.
NsNp=VsVp\frac{N_s}{N_p} = \frac{V_s}{V_p}
In an ideal transformer, the ratio of secondary-to-primary turns is directly proportional to the ratio of secondary-to-primary voltage.
3
Substitute the known values (Vs=600 VV_s = 600\text{ V}, Vp=120 VV_p = 120\text{ V}, and Np=150 turnsN_p = 150\text{ turns}) to solve for the secondary turns (NsN_s).
Ns=150×(600 V120 V)=150×5=750 turnsN_s = 150 \times \left(\frac{600\text{ V}}{120\text{ V}}\right) = 150 \times 5 = 750\text{ turns}
Multiplying the primary turns by the voltage scaling factor gives the required secondary turns.

Key Concept

Transformer turns ratio and multi-step AC secondary load calculations
Estimated Time:2m 0s
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Topics

Inductors and Transformers

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