In a step-up transformer the turn ratio is 1:10. A resistance of 200 ohm connected across the secondary is drawing a current of 0.5 A. What is the primary voltage and current?

Options

A. 50 V, 1 amp
B. 10 V, 5 amp
C. 25 V, 4 amp
D. 20 V, 2 amp

Explanation

To solve the problem step by step, we will use the properties of a step-up transformer and Ohm's law.

### Step 1: Calculate the Secondary Voltage (Vs)
Given:
- Resistance (R) = 200 ohms
- Current in the secondary (Is) = 0.5 A

Using Ohm's law:
\[ Vs = Is \times R \]
Substituting the values:
\[ Vs = 0.5 \, \text{A} \times 200 \, \Omega = 100 \, \text{V} \]

### Step 2: Use the Turn Ratio to Find the Primary Voltage (Vp)
The turn ratio (Np:Ns) is given as 1:10. This means:
\[ \frac{Np}{Ns} = \frac{1}{10} \]
For an ideal transformer, the voltage ratio is equal to the turn ratio:
\[ \frac{Vp}{Vs} = \frac{Np}{Ns} \]
Substituting the known values:
\[ \frac{Vp}{100 \, \text{V}} = \frac{1}{10} \]
Cross-multiplying gives:
\[ Vp = 100 \, \text{V} \times \frac{1}{10} = 10 \, \text{V} \]

### Step 3: Use the Turn Ratio to Find the Primary Current (Ip)
Using the current ratio, we know:
\[ \frac{Np}{Ns} = \frac{Is}{Ip} \]
Substituting the known values:
\[ \frac{1}{10} = \frac{0.5 \, \text{A}}{Ip} \]
Cross-multiplying gives:
\[ Ip = 0.5 \, \text{A} \times 10 = 5 \, \text{A} \]

### Final Answers
- Primary Voltage (Vp) = 10 V
- Primary Current (Ip) = 5 A