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1.Find the current in the 3.00 Ω resistor. (Note that three currents are given.)

2.Find the unknown emfs ε_{1} and ε_{2}.

3.Find the resistance R .

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Kirchhoff’s junction rule and Ohm’s law are the concepts that will solve this problem.

First, from the given currents, find the current in theresistor. Find the unknown emfs using Kirchhoff’s voltage law. Similar to the Kirchhoff voltage law, you can find the unknown resistance.

Ohm’s law says that the current between two points of a circuit is proportional the potential difference between them. The resistance is the constant of proportionality.

is the potential difference. is current, and #media_tag_4$ is resistance.

Kirchhoff’s circuit laws that govern current and voltage are used in electrical circuits. Kirchhoff’s current law says that the total amount of current entering a node is equal to its total output.

Kirchhoff’s voltage law says that the total voltage around closed loops is zero.

(26.23.1)Below is a diagram showing the current direction through the circuit.

The current in the lineand in the linecombine and flow together through the lineas current.

The current line is given by

Here, is the current in the lineandis the current in the line.

Substituteforandforto find the current.

(26.23.2.1)Kirchhoff’s voltage law is applied to loop .

Substituteforto find the emf.

The emf is

(26.23.2.2)Kirchhoff’s voltage law is applied to loop .

Substituteforto find the emf.

The emf is

(26.23.3)Kirchhoff’s voltage law is applied to loop .

Substituteforand forto find the resistance.

Ans: Part 26.3.1

The current in the is

Part 26.23.2.1

The emfis

Part 26.23.2.2

The emfis

Part 26.23.3

The resistanceis.