Three identical resistors connected in series with a...

Three identical resistors connected in series with a battery, together dissipate $10 \mathrm{~W}$ of power. What will be the power dissipated, if the same resistors are connected in paralle1 across the same battery? (A) $60 \mathrm{~W}$ (B) $30 \mathrm{~W}$ (C) $90 \mathrm{~W}$ (D) $120 \mathrm{~W}$

Three identical resistors connected in series with a battery, together dissipate $10 \mathrm{~W}$ of power. What will be the power dissipated, if the same resistors are connected in paralle1 across the same battery?
(A) $60 \mathrm{~W}$
(B) $30 \mathrm{~W}$
(C) $90 \mathrm{~W}$
(D) $120 \mathrm{~W}$

Key Concepts

Series and Parallel Circuits

Understanding how components are arranged in a circuit is crucial. In a series circuit, components are connected end-to-end so that the same current flows through each, while in a parallel circuit, all components are connected across the same voltage source and the voltage across each is equal. The configuration affects the overall resistance and the behavior of current in the circuit.

Equivalent Resistance

Calculating equivalent resistance simplifies the analysis of circuits with multiple resistors. For resistors in series, the equivalent resistance is the sum of the individual resistances, whereas for resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of each resistor's resistance. This concept is fundamental for predicting how a circuit will respond under a given voltage.

Ohm's Law

Ohm's Law, represented by the equation V = IR, relates the voltage across a resistor to the current flowing through it and its resistance. This principle is essential for analyzing circuits and determining unknown quantities when two of the three variables (voltage, current, resistance) are known.

Power Dissipation in Resistors

Power dissipation in electrical circuits, particularly in resistors, is a measure of the energy converted to heat. The power can be calculated using formulas such as P = V^2/R or P = I^2R. This concept is crucial when evaluating how changes in resistance or circuit configuration affect the energy utilized or dissipated by the circuit.

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