Three electric bulbs with markings 100 V-150 W, 100V-400W and 100V-500W are connected in series along power supply of 100V. Calculate the current in the circuit through each bulb.

Answer

To solve the problem of finding the current in a circuit with three electric bulbs connected in series, we will follow these steps:

### Step 1: Determine the Resistance of Each Bulb
The resistance of each bulb can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
where \( V \) is the voltage rating of the bulb and \( P \) is the power rating.

1. **For the first bulb (100 V, 150 W)**:
\[ R_1 = \frac{100^2}{150} = \frac{10000}{150} = 66.67 \, \Omega \]

2. **For the second bulb (100 V, 400 W)**:
\[ R_2 = \frac{100^2}{400} = \frac{10000}{400} = 25 \, \Omega \]

3. **For the third bulb (100 V, 500 W)**:
\[ R_3 = \frac{100^2}{500} = \frac{10000}{500} = 20 \, \Omega \]

### Step 2: Calculate the Total Resistance in the Circuit
Since the bulbs are connected in series, the total resistance \( R_{eq} \) is the sum of the individual resistances:
\[ R_{eq} = R_1 + R_2 + R_3 \]
Substituting the values we calculated:
\[ R_{eq} = 66.67 + 25 + 20 = 111.67 \, \Omega \]

### Step 3: Calculate the Current in the Circuit
Using Ohm's Law, the current \( I \) in the circuit can be calculated using the formula:
\[ I = \frac{V}{R_{eq}} \]
where \( V \) is the total voltage supplied (100 V):
\[ I = \frac{100}{111.67} \approx 0.896 \, A \]

### Final Answer
The current flowing through each bulb in the circuit is approximately:
\[ I \approx 0.9 \, A \]

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