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Zorluk: KolayInductors and Transformers

A control transformer in an HVAC system steps down an input line voltage of 240 V240\text{ V} AC to an output voltage of 24 V24\text{ V} AC to safely power a thermostat circuit. If the primary winding consists of 800800 turns of wire, what is the number of turns on the secondary winding?

Cevap: 80 turns

Cevap

80 turns
The secondary winding requires 80 turns. According to the transformer turns ratio relationship, VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}. Since the secondary voltage (24 V24\text{ V}) is one-tenth of the primary input voltage (240 V240\text{ V}), the secondary coil must have one-tenth the number of turns of the primary coil: 800×0.10=80800 \times 0.10 = 80 turns.

Adım Adım Çözüm

1
Identify known electrical parameters from the problem statement.
Vp=240 VV_p = 240\text{ V}, Vs=24 VV_s = 24\text{ V}, and Np=800 turnsN_p = 800\text{ turns}.
Establishing the input and output parameters is necessary to set up the transformer relationship.
2
Set up the ideal transformer turns ratio equation relating voltage and turns.
VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}
The voltage induced across transformer windings is directly proportional to the number of turns in each coil.
3
Rearrange the equation to isolate the unknown secondary winding turns (NsN_s).
Ns=Np×(VsVp)N_s = N_p \times \left(\frac{V_s}{V_p}\right)
Algebraic isolation allows direct computation of secondary turns.
4
Substitute the known numerical values into the formula and calculate the result.
Ns=800×(24 V240 V)=800×0.10=80 turnsN_s = 800 \times \left(\frac{24\text{ V}}{240\text{ V}}\right) = 800 \times 0.10 = 80\text{ turns}
Carrying out the arithmetic yields the exact number of secondary turns required.

Anahtar Kavram

Transformer Turns Ratio and Voltage Transformation

Alternatif Yöntem

Calculate the turns-per-volt ratio of the primary coil: 800 turns240 V=103 turns/V\frac{800\text{ turns}}{240\text{ V}} = \frac{10}{3}\text{ turns/V}. Then multiply by the desired secondary voltage: 24 V×103 turns/V=80 turns24\text{ V} \times \frac{10}{3}\text{ turns/V} = 80\text{ turns}.
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Inductors and Transformers

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