Consider four circuits shown in the figure below. In which circuit power dissipated is greatest? (Neglect the internal resistance of the power supply).
Show Hint
Maximum power when equivalent resistance is minimum.
To determine in which circuit the power dissipated is greatest, we need to understand the basic principle of power dissipation in resistive circuits. The power dissipated in a circuit is given by the formula:
\(P = \frac{V^2}{R}\)
where \(P\) is the power, \(V\) is the voltage, and \(R\) is the resistance.
Assuming the voltage across each circuit is the same, the resistance will determine the power dissipated. Lower resistance results in higher power dissipation.
In Circuit A: There are two resistors in parallel, which reduces the equivalent resistance. The formula for equivalent resistance in parallel is:
In Circuit B: There is only one resistor, so the resistance is highest here.
In Circuit C: This is a combination of parallel and series. The parallel portion will reduce the resistance but not as much as Circuit A.
In Circuit D: Similar to Circuit A in terms of parallel configuration, but exact resistances would need to reduce more to compare precisely.
Since Circuit A has purely parallel resistors, the equivalent resistance is significantly reduced:
\(R_{eqA} < R_{other\ circuits}\)
Thus, the power dissipated is maximum in Circuit A because resistance is minimized, making \(P_{A} = \frac{V^2}{R_{eqA}}\) the largest.
