What would be the total power drawn from the supply, when two heaters, rated at 1000 W, 250 V each are connected in series across a 250 V, 50 Hz supply?

Explanation:

Power Drawn by Two Heaters Connected in Series:

Problem Statement: We are tasked with determining the total power drawn from a 250 V, 50 Hz supply when two heaters, each rated at 1000 W, 250 V, are connected in series. Let us analyze the situation step-by-step.

Step 1: Understanding Heater Ratings

• Each heater is rated at 1000 W and 250 V. This means that when a heater is connected across a 250 V supply, it will draw 1000 W of power.
• The resistance of each heater can be calculated using the formula:

R = V² / P

• For a single heater:

R = (250)² / 1000 = 62500 / 1000 = 62.5 Ω

Thus, the resistance of each heater is 62.5 Ω.

Step 2: Connection in Series

• When the two heaters are connected in series, the total resistance (R_total) is the sum of their individual resistances:

R_total = R₁ + R₂

• Substituting the resistance values:

R_total = 62.5 Ω + 62.5 Ω = 125 Ω

Therefore, the total resistance of the circuit is 125 Ω.

Step 3: Current Flowing in the Series Circuit

• The current flowing through the circuit can be calculated using Ohm's Law:

I = V / R_total

• Substituting the values:

I = 250 V / 125 Ω = 2 A

Thus, the current flowing through the circuit is 2 A.

Step 4: Power Drawn from the Supply

• The total power drawn from the supply can be calculated using the formula:

P_total = V × I

• Substituting the values:

P_total = 250 V × 2 A = 500 W

Therefore, the total power drawn from the supply is 500 W.

Correct Option: Option 2 (500 W)

Additional Information

To further understand the problem, let’s analyze why the other options are incorrect:

Option 1 (1000 W):

This option assumes that the total power drawn from the supply is equal to the power rating of a single heater. However, since the two heaters are connected in series, the voltage is divided between them, and the total power drawn is reduced. Hence, this option is incorrect.

Option 3 (250 W):

This option underestimates the power drawn from the supply. The actual power drawn is 500 W, as calculated above. Hence, this option is also incorrect.

Option 4 (2000 W):

This option assumes that the two heaters draw their full rated power (1000 W each) simultaneously. However, this is not possible in a series connection because the voltage is shared between the heaters, and the current is the same through both. Therefore, this option is incorrect.

Conclusion:

When two heaters are connected in series across a 250 V supply, the total power drawn is 500 W. This result highlights the importance of considering the circuit configuration (series or parallel) when calculating power consumption. Series connections lead to reduced power consumption compared to individual operation, as the voltage is divided among the components, and the total resistance increases.