A resistor R1 consumes electrical power P1 when connected to an emf ℰ When resistor R2 is connec

step 1 We are given two resistors, R1 and R2, and that when they're connected to an EMF of Epsilon, the

A resistor R1 consumes electrical power P1 when connected to...

A resistor $R_{1}$ consumes electrical power $P_{1}$ when connected to an emf $\mathcal{E}$ When resistor $R_{2}$ is connected to the same emf, it consumes electrical power $P_{2}$ . In terms of $P_{1}$ and $P_{2},$ what is the total electrical power consumed when they are both connected to this emf source (a) in parallel and (b) in series?

A resistor $R_{1}$ consumes electrical power $P_{1}$ when connected to an emf $\mathcal{E}$ When resistor $R_{2}$ is connected to the same emf, it consumes electrical power $P_{2}$ . In terms of $P_{1}$ and $P_{2},$ what is the total electrical power consumed when they are both connected to
this emf source (a) in parallel and (b) in series?

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits which states that the voltage (V) across a resistor is proportional to the current (I) flowing through it, with the proportionality constant being the resistance (R) of the resistor, expressed by the equation V = IR. This law is essential for analyzing how voltages, currents, and resistances interact in circuits, both simple and complex.

Electrical Power in Resistive Circuits

Electrical power in resistive circuits is given by the formula P = V²/R, which shows the relationship between the power consumed by a resistor, the voltage applied, and its resistance. This concept allows us to understand how variations in resistance affect the power consumption when a constant voltage is applied, providing a means to relate different resistors’ power ratings under the same voltage source.

Series Circuits

In series circuits, components are connected one after another so that the same current flows sequentially through each component. The total or equivalent resistance is the sum of the individual resistances. This configuration affects the overall power consumption because the increased resistance results in a lower current and, therefore, lower total power drawn from a constant voltage source.

Parallel Circuits

In parallel circuits, components are connected across the same voltage source, allowing each component to have the same voltage across it. The total or equivalent resistance is found by taking the reciprocal of the sum of the reciprocals of the individual resistances, leading to a lower net resistance compared to any individual resistor. This causes an increase in the overall power consumption when connected to a constant voltage source, as the lower resistance allows more current to flow through the circuit.

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