A line having a total resistance of `0.5Omega` deliver 15kW at 240 V to a small factory . The efficiency of transmission is :

Options

A. `60%`
B. `79%`
C. `89%`
D. `97%`

Answer

To find the efficiency of the transmission of electrical power to the factory, we can follow these steps:

### Step 1: Calculate the Output Power
The output power delivered to the factory is given as 15 kW. We convert this to watts:
\[ P_{\text{output}} = 15 \, \text{kW} = 15 \times 1000 \, \text{W} = 15000 \, \text{W} \]

### Step 2: Calculate the Current in the Line
Using the formula for power, we can find the current (I) flowing through the line. The formula for power is:
\[ P = V \times I \]
Rearranging this gives:
\[ I = \frac{P}{V} \]
Substituting the values:
\[ I = \frac{15000 \, \text{W}}{240 \, \text{V}} = 62.5 \, \text{A} \]

### Step 3: Calculate the Power Loss in the Line
The power loss (P_loss) due to the resistance of the line can be calculated using the formula:
\[ P_{\text{loss}} = I^2 \times R \]
Where R is the resistance of the line (0.5 Ω). Substituting the values:
\[ P_{\text{loss}} = (62.5 \, \text{A})^2 \times 0.5 \, \Omega = 3906.25 \, \text{W} \]

### Step 4: Calculate the Total Power Supplied
The total power supplied (P_total) to the line is the sum of the output power and the power loss:
\[ P_{\text{total}} = P_{\text{output}} + P_{\text{loss}} = 15000 \, \text{W} + 3906.25 \, \text{W} = 18906.25 \, \text{W} \]

### Step 5: Calculate the Efficiency
The efficiency (η) of the transmission can be calculated using the formula:
\[ \eta = \left( \frac{P_{\text{output}}}{P_{\text{total}}} \right) \times 100 \]
Substituting the values:
\[ \eta = \left( \frac{15000 \, \text{W}}{18906.25 \, \text{W}} \right) \times 100 \approx 79.3\% \]

### Final Result
The efficiency of transmission is approximately **79.3%**.