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Question

Part A:

What is the current through the 10Ω resistor in the figure (Figure 1)?  

Part B :

Is the current from left to right or right to left?  

• Left to right  
• Right to left

Answer “What is the current through the 10 Ohm resistor in the figure (Figure 1)?”.

Concepts and reason

Kirchhoff’s law and the circuit diagram are the concepts that were used to answer the question.

First draw the circuit diagram. Next, show the direction that the current flows through each loop. Next, determine the current through each loop using Kirchhoff’s loop law.

Fundamentals

Kirchhoff’s Voltage law

The sum of all voltage drops in an open loop in an electrical circuit will equal the sum of all EMFs in the loop.

This law states that the sum of the potential differences in any closed circuit is zero.

Therefore,

Let us consider a circuit below

The circuit has two resistors R₁ ​and R_2​

To the circuit above, apply Kirchhoff’s voltage law.

Answer and Explanation:

Part A: Below is the circuit diagram

Let the current flowing through the circuit’s two loops be I₁ and I₂.

Apply the Kirchhoff’s law to the above circuit.

For the loop 1.

12 + 5I₁ ​+ 3 + 10I₁ ​− 10I_2​ = 0

15 + 5I₁ ​− 10I₂ ​= 0

15I₁​ = 10I₂​−15​

For the loop 2.

9 + 5I₂ ​+ 10I₂ ​− 10I₁​ − 3 = 0

6 + 15I₂ ​− 10I₁​ = 0 …… (2)

Substitute, the equation (1) in (2):

Substitute, – 1.92A −1.92A for I₂​ in the equation (1).

The current through the resistor 10Ω is

I₁₀ = I₁ – I₂

= – 2.28A – (- 1.92A)

= – 0.36A

The current direction that we chose was from the positive to the negative terminal was not correct.

Hence, the current through 10Ω is 0.36A .

Part B:

We chose the direction of the circuit from the positive to the negative terminal. The 10Ω resistor’s negative sign shows that we were wrong about the current direction.

The direction of current in 10Ω goes from negative to positive terminals. It is also from left to right.

Last words

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