# Application of Circuit laws (KCL and KVL)

• hms.tech
In summary, the resistance of this combination of resistors can be calculated by using the equation R=V/I, where I is equal to I5 + I2 + I4. This can be derived from the first equation which relates currents I2, I4, and I5 to the potential across the circuit. By substituting these expressions for the currents in the first equation, you can solve for I and then use that value to calculate the resistance.
hms.tech

## Homework Statement

Calculate the resistance of this combination of resistors

V=IR

## The Attempt at a Solution

By using KVL :

V= 3$I_{5}$ = $I_{2}$ = 2$I_{4}$
I = $I_{1}$ + $I_{2}$
$I_{3}$ = $I_{2}$ + $I_{4}$
$I_{1}$ = $I_{5}$ + $I_{4}$
I = $I_{3}$ + $I_{5}$Now the final result could be obtained by the simple equation : R =V/I (this is where my progress stagnates)

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Your first equation relates currents I2, I4, and I5 to the potential across the circuit. Now, if you take your last equation and make substitutions so that you express I in terms of those same currents in the first expression, I think you'll get somewhere.

You mean like this :

I = $I_{5}$ + $I_{2}$ + $I_{4}$

Thus R = V/I

that does not solve the problem ...

hms.tech said:
You mean like this :

I = $I_{5}$ + $I_{2}$ + $I_{4}$

Thus R = V/I

that does not solve the problem ...

But you can substitute your expressions for those currents from your first equation...

Oh yes, I overlooked this .
Thanks you

## 1. What is Kirchhoff's Current Law (KCL) and how is it applied in circuits?

Kirchhoff's Current Law states that the sum of currents entering and exiting a node (junction) in a circuit must be equal to zero. This means that the amount of current flowing into a node must be equal to the amount of current flowing out of the node. It is applied in circuits by using this principle to analyze and solve for unknown currents in a circuit.

## 2. How is Kirchhoff's Current Law different from Kirchhoff's Voltage Law (KVL)?

Kirchhoff's Voltage Law states that the algebraic sum of voltages in a closed loop in a circuit must be equal to zero. This means that the sum of voltage drops (negative) and voltage rises (positive) around a closed loop must equal zero. KCL and KVL are different laws that are used together to analyze and solve circuits.

## 3. Can Kirchhoff's Circuit Laws be applied to both AC and DC circuits?

Yes, Kirchhoff's Circuit Laws can be applied to both AC (alternating current) and DC (direct current) circuits. These laws are based on fundamental principles of circuit analysis and can be applied to any type of circuit.

## 4. What are some real-world applications of Kirchhoff's Circuit Laws?

Kirchhoff's Circuit Laws are widely used in various fields such as electrical engineering, physics, and electronics. Some real-world applications include circuit analysis and design, electronic circuit troubleshooting, and power distribution system analysis.

## 5. Are there any limitations to Kirchhoff's Circuit Laws?

While Kirchhoff's Circuit Laws are fundamental principles that are widely used in circuit analysis, they do have some limitations. These laws assume ideal conditions such as linear, time-invariant circuit elements and negligible parasitic effects. In some complex circuits, these assumptions may not hold true and more advanced techniques may be necessary for analysis.

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