# How Do You Calculate Power Dissipation in a Double Loop Circuit?

• j_baby
In summary, the conversation discusses a double loop circuit with two Emfs and a 7Ω resistor. The conversation includes attempts at solving the problem using Kirchhoff's laws and asks for clarification on the proper approach.
j_baby

## Homework Statement

A double loop circuit is shown in the figure below.

The Emf εx = 7.00 V and the Emf εw = 17.00 V. Both are shown on the diagram. Calculate the power dissipated in the 7 Ω resistor located on the extreme right in the circuit.

## The Attempt at a Solution

I always get confused with the direction this goes. I start out with the joint rule.
I1= I2 + I3 + I4 + I5 + I6

say I1 = the amps going through the seven ohm resister
I2 = " " that going through bottom 2 ohm
I3 = " " middle 4 ohm
I4 = " " middle 5 ohm
I5 = " " upper 4 ohm
I6 = " " left 2 ohm

Then I do one loop, say the rightmost
-7*I1 - 2*I2 - 4*I3 + 7V - 5*I4 - 17V = 0

then the right most loop
5*I4 -7V + 4*I3 - 2*I6 - 4*I5 = 0

is this the right way or completely wrong? any help would GREATLY be appreciated.. soon hah

#### Attachments

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There are only 3 unknown currents in this circuit. The current through Ex and de 4 ohm and 5 ohm resistor above and below it is obviously the same. The same goes for the 4 and 2 ohms resistors on the left, and Ew and the 2 and 7 ohms resistors on the right

Kirchhoffs current law will give you one relationship between those currents. and using the voltage law on 2 loops will give you two more.

ah

I would like to provide a clear and concise explanation of how to approach this double loop circuit problem. First, it is important to understand the basic principles of circuits and how to apply them in solving problems. In this case, we have two loops in the circuit, each containing multiple resistors and EMFs. To solve for the power dissipated in the 7 Ω resistor, we can use the power formula P = I^2*R, where I is the current flowing through the resistor and R is the resistance of the resistor.

To find the current flowing through the 7 Ω resistor, we can use the junction rule, which states that the total current entering a junction must equal the total current leaving the junction. In this case, the current entering the junction is I1, and the currents leaving the junction are I2, I3, I4, I5, and I6. So we can write the equation I1 = I2 + I3 + I4 + I5 + I6.

Next, we can apply Kirchhoff's voltage law (KVL) to each loop in the circuit. KVL states that the sum of all the voltages around a closed loop must equal zero. Using this law, we can write equations for each loop in the circuit. For the rightmost loop, we have -7*I1 - 2*I2 - 4*I3 + 7V - 5*I4 - 17V = 0. Similarly, for the leftmost loop, we have 5*I4 - 7V + 4*I3 - 2*I6 - 4*I5 = 0.

We now have two equations with two unknowns (I1 and I4), which we can solve to find the values of these currents. Once we have the value of I1, we can plug it into the power formula P = I^2*R to find the power dissipated in the 7 Ω resistor on the extreme right in the circuit.

In summary, to solve this double loop circuit problem, we need to apply the junction rule and Kirchhoff's voltage law to determine the currents in the circuit, and then use the power formula to find the power dissipated in the 7 Ω resistor. It is important to approach the problem systematically and use the correct equations to ensure accurate results. I hope this explanation helps in solving the problem.

## What is a double loop circuit?

A double loop circuit is an electrical circuit that contains two separate closed loops. This means that there are two paths for the electric current to flow through the circuit.

## What are the components of a double loop circuit?

The components of a double loop circuit include a power source, such as a battery, two separate loops of conductive material, and various resistors, capacitors, and other components that may be necessary for the circuit to function properly.

## What is the purpose of a double loop circuit?

A double loop circuit is often used in more complex electrical systems to allow for multiple pathways for the current to flow. This can be useful for creating different levels of power or controlling the flow of electricity in a more precise manner.

## How do you solve a double loop circuit problem?

Solving a double loop circuit problem involves using Kirchhoff's laws, which state that the sum of the currents entering a node (junction) in a circuit must equal the sum of the currents leaving the node. By applying these laws and using Ohm's law, you can calculate the values of the different components in the circuit.

## What are some common challenges when working with double loop circuits?

Some common challenges when working with double loop circuits include ensuring that the two loops do not interfere with each other, accurately calculating the values of the components, and properly connecting all the components in the circuit to avoid any breaks or interruptions in the flow of current.

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