The number of turns in primary coil a transformer is 20 and the number of turns in a secondary is 10. If the voltage across the primary is 220 ac V. What is the voltage across secondary?

Options

A. 100 ac V
B. 120 ac V
C. 110 ac V
D. 220 ac V

Explanation

To solve the problem, we will use the relationship between the voltages and the number of turns in the primary and secondary coils of a transformer. The formula we will use is:

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

where:
- \(V_s\) = voltage across the secondary coil
- \(V_p\) = voltage across the primary coil
- \(N_s\) = number of turns in the secondary coil
- \(N_p\) = number of turns in the primary coil

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Number of turns in primary coil, \(N_p = 20\)
- Number of turns in secondary coil, \(N_s = 10\)
- Voltage across primary, \(V_p = 220 \, \text{V}\)

**Step 2: Write the transformer equation.**
Using the transformer equation:
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \]

**Step 3: Substitute the known values into the equation.**
Substituting the known values into the equation:
\[ \frac{V_s}{220} = \frac{10}{20} \]

**Step 4: Simplify the fraction on the right side.**
The fraction \(\frac{10}{20}\) simplifies to \(\frac{1}{2}\):
\[ \frac{V_s}{220} = \frac{1}{2} \]

**Step 5: Solve for \(V_s\).**
To find \(V_s\), multiply both sides by 220:
\[ V_s = \frac{1}{2} \times 220 \]
\[ V_s = 110 \, \text{V} \]

**Step 6: State the final answer.**
The voltage across the secondary coil is \(110 \, \text{V}\).

### Final Answer:
The voltage across the secondary is \(110 \, \text{AC V}\).

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