The primary winding of a transformer has 500 turns whereas its secondary has 5000 turns. The primary is connected to an A.C. supply 20 V, 50 Hz. The secondary will have an output of

Question

Which of the following correctly represents the AND logic gate?

Answer 1

To solve the given problem, we need to use the concept of the transformer, where the relationship between the primary and secondary windings is given by the transformer turns ratio formula:

\frac{V_s}{V_p} = \frac{N_s}{N_p}

\(V_s\) is the secondary voltage
\(V_p\) is the primary voltage
\(N_s\) is the number of turns in the secondary winding
\(N_p\) is the number of turns in the primary winding

Given values in the question:

Primary voltage, \(V_p = 20 \text{ V}\)
Number of turns in the primary winding, \(N_p = 500\)
Number of turns in the secondary winding, \(N_s = 5000\)

We need to calculate the secondary voltage, \(V_s\). Substitute the known values into the formula:

\frac{V_s}{20} = \frac{5000}{500}

Simplifying the right-hand side:

\frac{5000}{500} = 10

Thus, the equation becomes:

\frac{V_s}{20} = 10

Solving for \(V_s\):

V_s = 20 \times 10 = 200 \text{ V}

Therefore, the secondary voltage is \(200 \text{ V}\).

Additionally, since the frequency of both primary and secondary windings in a transformer remains the same, the frequency of the secondary winding is also \(50 \text{ Hz}\).

Thus, the secondary will have an output of 200 V, 50 Hz.

Hence, the correct answer is: 200 V, 50 Hz

The other options are incorrect because:

2 V, 50 Hz: Incorrect, as the secondary voltage calculated is 200 V, not 2 V.
2 V, 5 Hz: Incorrect, both voltage and frequency values are wrong.
200 V, 500 Hz: Incorrect, while the voltage is calculated correctly, the frequency does not change due to the transformer operation, it remains 50 Hz.

Answer 2