Find the current in the 3.00 ω resistor. (note that three currents are given.) 26.23)

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

2.Find the unknown emfs and .

3.Find the resistance .

General guidance

Concepts and reason
The concepts required to solve the problem are Ohm’s law and Kirchhoff’s junction rule.

First, from the given currents, find the current in the resistor. Using Kirchhoff’s voltage law, find the unknown emfs. Similarly, using the Kirchhoff’s voltage law, find the unknown resistance.

Fundamentals

Ohm’s law states that current between two points in a circuit is proportional to the potential difference between the points. The constant of proportionality is called the resistance. Here, is the potential difference, is the current and is the resistance.

Kirchhoff’s circuit laws for current and voltage are applied in electrical circuits. Kirchhoff’s current law states that the total current entering a nod is equal to the total current leaving the node.

Kirchhoff’s voltage law states that the total voltage around a closed loop is zero.

Step-by-step

Step 1 of 4

(26.23.1)

The below figure shows the direction of current flowing through the circuit. The current in the line and in the line combine and flow together through the line as current .

So, the current in the line is given by Here, is the current in the line and is the current in the line .

Substitute for and for to find the current . Part 26.23.1

The current in the is The current through the resistor is the sum of the current through the resistor and through the resistor.

Step 2 of 4

(26.23.2.1)

Applying Kirchhoff’s voltage law in loop , Substitute for to find the emf . So, the emf is Part 26.23.2.1

The emf is According to Kirchhoff’s second law, the voltage at a closed loop is zero. Applying this law in the loop , the emf is the sum of the products of the current and resistor in wire and the current and resistor in wire .

Step 3 of 4

(26.23.2.2)

Applying Kirchhoff’s voltage law in loop , Substitute for to find the emf . So, the emf is Part 26.23.2.2

The emf is Applying Kirchhoff’s second law in the loop , the emf is the sum of the products of the current and resistor in wire and the current and resistor in wire .

Step 4 of 4

(26.23.3)

Applying Kirchhoff’s voltage law in loop , Substitute for and for to find the resistance . Part 26.23.3

The resistance is .

Applying Kirchhoff’s second law in the loop , the resistance is the sum emfs and .

Part 26.23.1

The current in the is Part 26.23.2.1

The emf is Part 26.23.2.2

The emf is Part 26.23.3

The resistance is .

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