A power transformer (step up) with an `1:8` turns ratio has `60 Hz,120 V` across the primary, the load in the secondary is `10^(4) Omega`.The current in the secondary is

Options

A. `96 A`
B. `0.96 A`
C. `9.6 A`
D. `96 mA`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Turns ratio of the transformer (Np:Ns) = 1:8
- Voltage across the primary (Vp) = 120 V
- Load resistance in the secondary (Rs) = 10^4 Ω (or 10,000 Ω)

### Step 2: Calculate the voltage across the secondary (Vs)
Using the transformer turns ratio, we can find the voltage in the secondary using the formula:

\[ \frac{Np}{Ns} = \frac{Vp}{Vs} \]

Given that \(Np/Ns = 1/8\), we can rearrange the formula to find \(Vs\):

\[ Vs = \frac{Ns}{Np} \cdot Vp = 8 \cdot Vp \]

Substituting the value of \(Vp\):

\[ Vs = 8 \cdot 120 V = 960 V \]

### Step 3: Calculate the current in the secondary (Is)
Using Ohm's law, the current in the secondary can be calculated as:

\[ Is = \frac{Vs}{Rs} \]

Substituting the values we have:

\[ Is = \frac{960 V}{10^4 Ω} = \frac{960}{10000} = 0.096 A \]

### Step 4: Convert the current to milliamperes
To convert the current from amperes to milliamperes, we multiply by 1000:

\[ Is = 0.096 A \times 1000 = 96 mA \]

### Final Answer
The current in the secondary is **96 mA**.

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