Hard 0 likes

Question

Three equal resistors connected in series across a source of e.m.f. together dissipate 10 W of power. What would be the power dissipated if the same resistors were connected in parallel across the same source of e.m.f.?

WBBSE Class X Physical Science Current Electricity 03 Mark 2025

Answer

Let each resistor be R.

When connected in series,

Equivalent resistance = 3R

Given, Power dissipated = 10 W

Using the formula, P = \frac{V^2}{R}

⇒ 10 = \frac{V^2}{3R}

⇒ V² = 10 × 3R = 30 R

When the same resistors are connected in parallel,

Equivalent resistance = \frac{R}{3}

Power (P) = \frac{V^2}{R/3} = \frac{3V^2}{R}

Substituting V² = 30R,

P = \frac{3 \times 30R}{R} = 90 W

Hence, the power dissipated in the parallel combination is 90 W.

Related Questions

More WBBSE Hard level questions

1/12
Hard
885
Q. The equivalent resistances of two conductors are 9 Ω and 2 Ω when they are...
A. For Series: R1 + R2 = 9 or, R1 = 9 -...
Hard
963
Q. Two metallic wires A and B of the same length are made of the same...
A. R = ρ or,R = ρ ⇒ R ∝ ⇒ = Given:...
Hard
951
Q. If two electric bulbs of ratings ‘240V-60 W’ and ‘240V-100W’ are connected in series, which...
A. Find resistance of each (R = V²/P): R₆₀ = 240² / 60...
Moderate
Q. The series combination of three 20 Ω resistances is connected in parallel combination to a...
A. Three resistors of 20 Ω each are connected in series. Resistance in...
Moderate
Q. State Lenz’s law. “Lenz’s law actually follows the principle of conservation of energy.” — Justify.
A. According to Lenz's law, whenever there is a change in magnetic flux,...
Easy
813
Q. Write down the difference between dynamo and electric motor. What is earthing?
A. Difference between Dynamo and Electric Motor: Feature Dynamo Electric Motor Function Converts...
Moderate
534
Q. Write Faraday’s laws of electromagnetic induction. Mention one advantage of using a LED lamp over...
A. Faraday's law of electromagnetic induction: Whenever there is a change in magnetic...
Easy
657
Q. State Ohm’s law. If a potential difference of 10 V is applied between the two...
A. Ohm's Law states that the current (I) flowing through a conductor is...
Easy
963
Q. Which energy is transformed to which energy in an electric motor? Why in domestic circuits,...
A. In an electric motor, electrical energy is transformed into mechanical energy. Domestic...
Easy
Q. State Fleming’s Left Hand Rule
A. Fleming's left-hand rule states that when you stretch the thumb, forefinger, and...
Moderate
Q. A thin wire of resistance 4 Ω is bent to form a circle. Find the...
A. Resistance of the complete wire = 4 Ω The wire is bent...
Easy
Q. Which one of the following is the unit of electrical energy?
A. (c) Kilowatt-hour (kWh)