How many 100 W, 200 V bulbs connected in series will consume same power as one 50W, 200 V bulb when connected across same voltage source assuming that filament properties are independent of voltage and temperature ?

The power consumed by a bulb is given by the formula: P = V² / R

Where:

• P = Power consumed
• V = Voltage across the bulb
• R = Resistance of the bulb

From the formula, we can derive the resistance of the bulb:

R = V² / P

Step 2: Resistance of the Bulbs

R₁ = V² / P = (200)² / 100 = 40000 / 100 = 400 Ω

R₂ = V² / P = (200)² / 50 = 40000 / 50 = 800 Ω

• For a 100 W, 200 V bulb:
• For a 50 W, 200 V bulb:

Step 3: Power Consumption of Bulbs in Series

When bulbs are connected in series, the total resistance is the sum of individual resistances. Let’s assume n bulbs of 100 W are connected in series. Then, the total resistance is:

Rₜ = n × R₁

Substitute the resistance of one 100 W bulb (R₁ = 400 Ω):

Rₜ = n × 400

The power consumed by the series combination is given by:

Pₜ = V² / Rₜ

Substitute Rₜ = n × 400:

Pₜ = V² / (n × 400)

We need this power (Pₜ) to be equal to the power consumed by the 50 W bulb (P₂ = 50 W). Thus:

50 = V² / (n × 400)

Substitute V = 200 V:

50 = (200)² / (n × 400)

50 = 40000 / (n × 400)

n × 400 = 40000 / 50

n × 400 = 800

n = 2

Thus, 2 bulbs of 100 W connected in series will consume the same power as one 50 W bulb when connected across the same voltage source.

Step 4: Verification

Let’s verify this calculation:

Rₜ = n × R₁ = 2 × 400 = 800 Ω

Pₜ = V² / Rₜ = (200)² / 800 = 40000 / 800 = 50 W

• Total resistance for 2 bulbs in series:
• Power consumed:

The power consumed matches the required value, confirming that the calculation is correct.

Correct Option:

The correct option is:

Option 1: 2