---
title: "Two identical lightbulbs, Bulb 1 and Bulb 2, each have a constant resistance \\(R\\). They are connected to an ideal battery of emf \\(\\varepsilon\\) in two different configurations. In Circuit 1, the two bulbs are connected in series with the battery. In Circuit 2, the two bulbs are connected in parallel with the battery."
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url: "https://nerd-notes.com/ubq/117683/"
date_modified: "2026-08-04T07:52:55+00:00"
---

# Two identical lightbulbs, Bulb 1 and Bulb 2, each have a constant resistance \(R\). They are connected to an ideal battery of emf \(\varepsilon\) in two different configurations. In Circuit 1, the two bulbs are connected in series with the battery. In Circuit 2, the two bulbs are connected in parallel with the battery.

Two identical lightbulbs, Bulb 1 and Bulb 2, each have a constant resistance \(R\). They are connected to an ideal battery of emf \(\varepsilon\) in two different configurations. In Circuit 1, the two bulbs are connected in series with the battery. In Circuit 2, the two bulbs are connected in parallel with the battery.

![A figure showing two circuit diagrams side by side. The left circuit is labeled 'Circuit 1' and consists of a rectangular wire loop with a battery symbol on the left vertical side, labeled \(\varepsilon\). The top horizontal wire contains two lightbulb symbols (circles with a looping filament inside) in series. The left bulb is labeled 'Bulb 1' and the right bulb is labeled 'Bulb 2'. The right circuit is labeled 'Circuit 2' and consists of a battery symbol on the left vertical wire, labeled \(\varepsilon\), connected to two parallel vertical branches on the right. The inner vertical branch contains a lightbulb symbol labeled 'Bulb 1' and the outer vertical branch contains a lightbulb symbol labeled 'Bulb 2'. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829974-LmEmSA.jpg)

**Part a)** A student claims that Circuit 2 will dissipate more total power than Circuit 1 because providing multiple paths for the current reduces the overall equivalent resistance of the circuit. **Evaluate** this claim qualitatively. **Justify** your answer using physical principles, without deriving or using equations. *(2 points)*

**Part b)** **Derive** expressions for the total power \(P_S\) dissipated by Circuit 1 and the total power \(P_P\) dissipated by Circuit 2. Express your answers in terms of \(\varepsilon\), \(R\), and fundamental constants. *(3 points)*

**Part c)** **Explain** how the expressions derived in part (b) support your qualitative reasoning in part (a). *(1 points)*

**Part d)** Suppose Bulb 1 in Circuit 2 burns out, creating an open circuit in that branch. *(4 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117683/*