A 220 V and 800 W electric kettle and three 220 V and 100 W bulbs are connected in parallel. On connecting this combination with 200 V supply, the total currentin the circuit will be

Options

A. 0.15 A
B. 0.20833333333333
C. 5.5 A
D. 4.55 A

Explanation

To solve the problem step by step, we need to calculate the total current in the circuit when the kettle and bulbs are connected in parallel to a 200 V supply.

### Step 1: Calculate the resistance of the electric kettle
The power \( P \) of the kettle is given as 800 W and the voltage \( V \) is 220 V. The resistance \( R_k \) of the kettle can be calculated using the formula:

\[ R_k = \frac{V^2}{P} \]

Substituting the values:

\[ R_k = \frac{220^2}{800} = \frac{48400}{800} = 60.5 \, \Omega \]

### Step 2: Calculate the resistance of one bulb
Each bulb has a power \( P \) of 100 W and the voltage \( V \) is 220 V. The resistance \( R_b \) of one bulb can be calculated similarly:

\[ R_b = \frac{V^2}{P} \]

Substituting the values:

\[ R_b = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 3: Calculate the equivalent resistance of the three bulbs in parallel
Since there are three identical bulbs, the equivalent resistance \( R_p \) of the three bulbs connected in parallel can be calculated using the formula for resistors in parallel:

\[ \frac{1}{R_p} = \frac{1}{R_b} + \frac{1}{R_b} + \frac{1}{R_b} = \frac{3}{R_b} \]

Thus,

\[ R_p = \frac{R_b}{3} = \frac{484}{3} \approx 161.33 \, \Omega \]

### Step 4: Calculate the total equivalent resistance in the circuit
The kettle and the equivalent resistance of the bulbs are in parallel. The total equivalent resistance \( R_{eq} \) can be calculated using:

\[ \frac{1}{R_{eq}} = \frac{1}{R_k} + \frac{1}{R_p} \]

Substituting the values:

\[ \frac{1}{R_{eq}} = \frac{1}{60.5} + \frac{1}{161.33} \]

Calculating each term:

\[ \frac{1}{R_{eq}} = \frac{161.33 + 60.5}{60.5 \times 161.33} \]

Calculating the denominator:

\[ 60.5 \times 161.33 \approx 9766.165 \]

Calculating the numerator:

\[ 161.33 + 60.5 \approx 221.83 \]

Thus,

\[ \frac{1}{R_{eq}} \approx \frac{221.83}{9766.165} \implies R_{eq} \approx \frac{9766.165}{221.83} \approx 44 \, \Omega \]

### Step 5: Calculate the total current in the circuit
Using Ohm's law, the total current \( I \) in the circuit can be calculated using:

\[ I = \frac{V}{R_{eq}} \]

Substituting the values:

\[ I = \frac{200}{44} \approx 4.55 \, \text{A} \]

### Final Answer
The total current in the circuit is approximately **4.55 A**.

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