The secondary coil of an ideal step down transformer is delivering 500 watt power at `12.5 A` current. If the ratio of turns in the primary to the secondary is `5 : 1` then the current flowing in the primary coil will be:

Options

A. 62.5 A
B. 2.5 A
C. 0.25
D. 0.4 A

Explanation

To find the current flowing in the primary coil of the transformer, we can follow these steps:

### Step 1: Understand the Power in the Transformer
The power delivered by the secondary coil (P) is given as 500 watts. In an ideal transformer, the power in the primary coil (Pp) is equal to the power in the secondary coil (Ps):
\[ P_p = P_s = 500 \text{ watts} \]

### Step 2: Use the Current in the Secondary Coil
The current in the secondary coil (Is) is given as 12.5 A. We can use this information to find the voltage in the secondary coil (Vs) using the power formula:
\[ P_s = V_s \cdot I_s \]
Rearranging gives us:
\[ V_s = \frac{P_s}{I_s} = \frac{500 \text{ watts}}{12.5 \text{ A}} = 40 \text{ volts} \]

### Step 3: Determine the Turns Ratio
The turns ratio of the transformer is given as:
\[ \frac{N_p}{N_s} = 5:1 \]
This means that for every 5 turns in the primary coil, there is 1 turn in the secondary coil.

### Step 4: Use the Turns Ratio to Find the Primary Voltage
In an ideal transformer, the voltage ratio is equal to the turns ratio:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
Thus, we can find the primary voltage (Vp):
\[ V_p = V_s \cdot \frac{N_p}{N_s} = 40 \text{ volts} \cdot 5 = 200 \text{ volts} \]

### Step 5: Calculate the Current in the Primary Coil
Using the power formula again for the primary coil:
\[ P_p = V_p \cdot I_p \]
We can rearrange this to find the primary current (Ip):
\[ I_p = \frac{P_p}{V_p} = \frac{500 \text{ watts}}{200 \text{ volts}} = 2.5 \text{ A} \]

### Final Answer
The current flowing in the primary coil is:
\[ I_p = 2.5 \text{ A} \]

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