Question

The primary coil of a transformer has N1 = 320 turns, and the secondary coil has N2 = 2 240 turns. If the input voltage across the primary coil is Δv(t) = 170 cos ωt, where Δv is in volts and t is in seconds, what rms voltage is developed across the secondary coil?

Answer 1

Answer:

The rms voltage across the secondary coil is 841.47 V

Explanation:

Given data:

N₁ = primary turns = 320

N₂ = secondary turns = 2240

From the input voltage

$delta-V=170coswt$

V₁max = 170 V

The rms primary voltage is:

$V_{1,rms} =\frac{V_{max} }{\sqrt{2} } =\frac{170}{\sqrt{2} } =120.21V$

$\frac{N_{1}}{N_{2} } =\frac{V_{1}}{V_{2}} \\\frac{320}{2240} =\frac{120.21}{V_{2}} \\V_{2}=841.47V$

Answer 2

Answer: 841.46 V

Explanation:

Given

No of turns of primary coil, N1 = 320

No of turns of secondary coil, N2 = 2240

Max input voltage, Max ΔV(in) = 170 V

Max output voltage, Max ΔV(out) = ?

Rms voltage across the coil, ΔV(rms) = ?

Then to start, we find

Max ΔV(out) = N2/N1 * Max ΔV(in)

Max ΔV(out) = 2240 / 320 * 170

Max ΔV(out) = 7 * 170 = 1190 V

Now, ΔV(rms) = Max ΔV(out) / √2

ΔV(rms) = 1190 / √2

ΔV(rms) = 1190 / 1.4142

ΔV(rms) = 841.46 V

Therefore, the rms voltage developed across the secondary coil is 841.46 V