A 50 Hz AC current of crest value 1 A flows through the primary of a transformer. If the mutual inductance between the primary and secondary is 0.5 H, the crest voltage induced in the secondary is______.
Fill in the blank with the correct answer from the options given below.

Question

Which of the following correctly represents the AND logic gate?

Answer 1

Analysis of induced voltage in the transformer's secondary coil.

1. Induced Voltage (ε_s):

The formula for the induced voltage in the secondary coil is:

ε_s = M(dI_p/dt)

Where:

2. Primary Current (I_p):

The primary current is defined as:

I_p = I₀sin(ωt)

Where:

Substituting the values:

I_p = 1 * sin(2π * 50 * t)

I_p = sin(100πt)

3. Rate of Change of Primary Current (dI_p/dt):

The derivative of the primary current with respect to time is:

dI_p/dt = d(sin(100πt))/dt

dI_p/dt = 100πcos(100πt)

4. Induced Voltage (ε_s):

Substituting the rate of change of current into the induced voltage formula:

ε_s = M(dI_p/dt)

ε_s = 0.5 H * 100πcos(100πt)

ε_s = 50πcos(100πt)

5. Crest Voltage (ε₀):

The maximum induced voltage (crest voltage) occurs when cos(100πt) = 1:

ε₀ = 50π V

Using π ≈ 3.14:

ε₀ = 50 * 3.14 V

ε₀ = 157 V

The calculated crest voltage induced in the secondary coil is approximately 157 V.

The closest available answer is 150 V.

The correct answer is:

Option 2: 150 V

The Correct Option is B