---
title: "In the circuit schematic shown, three vertical branches connect a top junction (Node \\(N\\)) to a grounded bottom wire (\\(0\\text{ V}\\)). The left branch contains a \\(20\\text{ V}\\) ideal battery (positive terminal facing Node \\(N\\)) and a \\(2.0\\text{ }\\Omega\\) resistor. The central branch contains a \\(4.0\\text{ V}\\) ideal battery (positive terminal facing Node \\(N\\)) and a \\(4.0\\text{ }\\Omega\\) resistor. The right branch contains a \\(12\\text{ V}\\) ideal battery (positive terminal facing the bottom wire) and a \\(4.0\\text{ }\\Omega\\) resistor. What is the magnitude and direction of the electric current in the central branch?"
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url: "https://nerd-notes.com/ubq/118428/"
date_modified: "2026-08-04T08:10:01+00:00"
---

# In the circuit schematic shown, three vertical branches connect a top junction (Node \(N\)) to a grounded bottom wire (\(0\text{ V}\)). The left branch contains a \(20\text{ V}\) ideal battery (positive terminal facing Node \(N\)) and a \(2.0\text{ }\Omega\) resistor. The central branch contains a \(4.0\text{ V}\) ideal battery (positive terminal facing Node \(N\)) and a \(4.0\text{ }\Omega\) resistor. The right branch contains a \(12\text{ V}\) ideal battery (positive terminal facing the bottom wire) and a \(4.0\text{ }\Omega\) resistor. What is the magnitude and direction of the electric current in the central branch?

In the circuit schematic shown, three vertical branches connect a top junction (Node \(N\)) to a grounded bottom wire (\(0\text{ V}\)). The left branch contains a \(20\text{ V}\) ideal battery (positive terminal facing Node \(N\)) and a \(2.0\text{ }\Omega\) resistor. The central branch contains a \(4.0\text{ V}\) ideal battery (positive terminal facing Node \(N\)) and a \(4.0\text{ }\Omega\) resistor. The right branch contains a \(12\text{ V}\) ideal battery (positive terminal facing the bottom wire) and a \(4.0\text{ }\Omega\) resistor. What is the magnitude and direction of the electric current in the central branch?

![A circuit schematic consisting of three vertical parallel branches connected at top and bottom by horizontal wires. The bottom horizontal wire is connected to a ground symbol labeled 0 V. The left vertical branch contains an ideal battery labeled \varepsilon_1 = 20\text{ V} with its longer positive plate on top, connected in series with a resistor labeled R_1 = 2.0\text{ }\Omega. The central vertical branch contains an ideal battery labeled \varepsilon_2 = 4.0\text{ V} with its longer positive plate on top, connected in series with a resistor labeled R_2 = 4.0\text{ }\Omega. The right vertical branch contains an ideal battery labeled \varepsilon_3 = 12\text{ V} with its longer positive plate on the bottom, connected in series with a resistor labeled R_3 = 4.0\text{ }\Omega. The top node connecting the three branches is labeled Node N. No other labels, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831001-wb00jl.jpg)

- **A.** \(0.50\text{ A}\), directed upward
- **B.** \(1.0\text{ A}\), directed downward
- **C.** \(1.0\text{ A}\), directed upward
- **D.** \(2.0\text{ A}\), directed downward

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118428/*