Power Dissipated in a Circuit: Problem Solving

Total power supplied by the battery equals the product of total current and source voltage. First, find equivalent resistance using the parallel resistance formula, then apply Ohm's law to determine total current. Multiply this current by the battery's emf to get total power in watts. This value should equal the sum of power dissipated by individual resistors, confirming energy conservation.

In a parallel circuit, all resistor leads connect directly to the same two points, creating identical potential differences across each resistor. This equal voltage distribution is a fundamental characteristic of parallel configurations. However, the current through each resistor varies based on its resistance value, determined by Ohm's law applied individually to each branch.

In a parallel circuit, equivalent resistance is smaller than any individual resistor value. The reciprocal of equivalent resistance equals the sum of reciprocals of individual resistances. This inverse relationship means adding resistors in parallel decreases total resistance, allowing more current to flow from the battery compared to series configurations.

Power dissipated by each resistor depends on its resistance value and the voltage across it. Since all resistors receive the same voltage in parallel, lower resistance values dissipate more power. Using P = V²/R, a one-ohm resistor dissipates more power than a four-ohm resistor at identical voltage, demonstrating the inverse relationship between resistance and power dissipation.

Energy conservation requires that all power supplied by the battery is dissipated as heat in the resistors. The battery converts chemical energy into electrical energy, which resistors convert to thermal energy. Summing individual power dissipations yields the total battery power, confirming no energy is lost or created in the circuit, only transformed.

Apply Ohm's law to each resistor individually: I = V/R. Since all resistors experience the same voltage in parallel, divide that voltage by each resistor's resistance to find its current. The sum of all individual currents equals the total current supplied by the battery, which can be verified using the equivalent resistance and total voltage.

Ohm's law (V = IR) is essential for finding current, voltage, and resistance relationships throughout the circuit. It determines total current from equivalent resistance and battery voltage, calculates individual resistor currents from shared voltage, and enables power calculations using P = VI or P = V²/R. This foundational relationship connects all circuit quantities needed for power analysis.