An 1800 W toaster, a 1.3 kW electric fan and a 100 W lamp are plugged in the same 120 V circuit i.e., all the three devices are in parallel. What is the approximate value of the total current (i.e. the sum of current drawn by the three devices) through the circuit ?

Options

A. 40 A
B. 120 A
C. 18 A
D. 27 A

Answer

To find the total current drawn by the toaster, electric fan, and lamp connected in parallel to a 120 V circuit, we can follow these steps:

### Step 1: Identify the power ratings of each device.
- Toaster: \( P_1 = 1800 \, \text{W} \)
- Electric Fan: \( P_2 = 1.3 \, \text{kW} = 1300 \, \text{W} \)
- Lamp: \( P_3 = 100 \, \text{W} \)

### Step 2: Calculate the total power consumed by the devices.
The total power \( P \) is the sum of the power ratings of all devices:
\[ P = P_1 + P_2 + P_3 = 1800 \, \text{W} + 1300 \, \text{W} + 100 \, \text{W} \]
\[ P = 3200 \, \text{W} \]

### Step 3: Use the power formula to find the total current.
The relationship between power, voltage, and current is given by:
\[ P = V \times I \]
Where:
- \( P \) is the total power (in watts)
- \( V \) is the voltage (in volts)
- \( I \) is the current (in amperes)

Rearranging the formula to solve for current \( I \):
\[ I = \frac{P}{V} \]

### Step 4: Substitute the values into the formula.
Given that the voltage \( V = 120 \, \text{V} \):
\[ I = \frac{3200 \, \text{W}}{120 \, \text{V}} \]

### Step 5: Calculate the total current.
\[ I = \frac{3200}{120} \approx 26.67 \, \text{A} \]

### Step 6: Round to the nearest whole number.
The approximate value of the total current is:
\[ I \approx 27 \, \text{A} \]

### Final Answer:
The total current drawn by the three devices is approximately **27 A**.

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