An electric bulb is marked 100W, 230V. If the supply voltage drops to 115V, what is the heat and light energy produced by the bulb in 20min? Calculate the current flowing through it.

Options

A. 10 kJ
B. 15 kJ
C. 20 kJ
D. 30 kJ

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Identify Given Values
- Power of the bulb (P) = 100 W
- Voltage rating of the bulb (V) = 230 V
- Reduced supply voltage (V') = 115 V
- Time (t) = 20 minutes

### Step 2: Convert Time to Seconds
Since the time is given in minutes, we need to convert it to seconds:
\[ t = 20 \text{ minutes} \times 60 \text{ seconds/minute} = 1200 \text{ seconds} \]

### Step 3: Calculate the Resistance of the Bulb
Using the formula for power:
\[ P = \frac{V^2}{R} \]
We can rearrange this to find the resistance (R):
\[ R = \frac{V^2}{P} \]
Substituting the values:
\[ R = \frac{(230)^2}{100} = \frac{52900}{100} = 529 \, \Omega \]

### Step 4: Calculate the Current at the Reduced Voltage
Using Ohm's Law:
\[ I = \frac{V'}{R} \]
Substituting the reduced voltage and the resistance:
\[ I = \frac{115}{529} \approx 0.217 \, A \]

### Step 5: Calculate the Power at the Reduced Voltage
Using the formula for power:
\[ P' = \frac{(V')^2}{R} \]
Substituting the reduced voltage and the resistance:
\[ P' = \frac{(115)^2}{529} = \frac{13225}{529} \approx 25 \, W \]

### Step 6: Calculate the Heat and Light Energy Produced
Using the formula:
\[ \text{Energy} = P' \times t \]
Substituting the power at reduced voltage and the time:
\[ \text{Energy} = 25 \, W \times 1200 \, s = 30000 \, J \]
Converting joules to kilojoules:
\[ \text{Energy} = 30 \, kJ \]

### Final Answers
- Current flowing through the bulb: \( I \approx 0.217 \, A \)
- Heat and light energy produced in 20 minutes: \( 30 \, kJ \)