# Basic Circuit Problems - KVL and KCL

• Engineering
• steven10137
In summary: So the current i2 will be assigned a negative sign, but that just means it's in the opposite direction of the assumed current direction. Therefore, when solving for R2 using V=IR, the negative sign will cancel out and you will still get a positive resistance value.
steven10137

## Homework Statement

Find $$R_2$$ in the circuit below.

http://img214.imageshack.us/img214/6396/circuithh3.jpg

## Homework Equations

Kirchoff's Current Law:
$$\sum {I_{IN} } = \sum {I_{OUT} }$$

Kirchoff's Voltage Law:
$$\sum {V = 0}$$

## The Attempt at a Solution

Using KCL for the node joining the 8ohm resistor, R2 and the 1 ohm resistor:
$$i_1 = i_2 + 2$$

Now using KVL for the shortest route down the 1 ohm resistor from the voltage source.
$$- 10 + 8i_1 + 2 = 0\; \Rightarrow \;i_1 = 1\;A$$

From the first equation;
$$i_2 = i_1 - 2 = 1 - 2 = - 1\;A$$Until this point, everything seems logical, and I think it is right.

Now in order to solve for $$R_2$$ I must now use $$V = IR$$ correct?

But, am I right in saying that because the voltage is flowing in the same direction and has changed by 2V, that the potential difference = 2V. Therefore $$R_2 = \frac{2}{{ - 1}} = - 2\;\Omega$$.
Resistance can't be negative though can it?

Can someone explain the situation in simple terms or what laws govern this?
I'm happy to read further if some people can give me some hints in the right direction.

Cheers
Steven.

Last edited by a moderator:
What is the voltage across the 1 ohm resistor?
R2 has one side connected with the 1 ohm resistor and the other connected to the 12V source. What is the voltage drop across it?

CEL said:
What is the voltage across the 1 ohm resistor?

V=IR = (2)(1) = 2V

CEL said:
R2 has one side connected with the 1 ohm resistor and the other connected to the 12V source. What is the voltage drop across it?

The Voltage drop is therefore 12 - 2 = 10V?

Knowing the voltage drop and the current through R2, you can calculate its value.

excellent cheers mate.

I was also shown another method today which involved more dependability on the sign conventions, but is more politically correct, yet yields the same result.

resistance can never be negative
but it coming negative because direction of current taken is opposite

you can call this beauty of kvl and kcl

steven10137 said:
Resistance can't be negative though can it?

Of course the resistance cannot be negative, but the problem is resolved by realizing the direction of the current is into the common node of the resistors, not away from it.

## 1. What is KVL (Kirchhoff's Voltage Law)?

Kirchhoff's Voltage Law states that the sum of all voltages in a closed loop in a circuit is equal to zero. This means that the total voltage supplied by the source must be equal to the voltage drops across all the components in the loop.

## 2. What is KCL (Kirchhoff's Current Law)?

Kirchhoff's Current Law states that the sum of all currents entering and leaving a node in a circuit is equal to zero. This means that the total current flowing into a node must be equal to the total current flowing out of the node.

## 3. How do I apply KVL and KCL to solve basic circuit problems?

To apply KVL and KCL, you need to first draw a circuit diagram and label all the components and their respective voltages and currents. Then, use KVL to write equations for each closed loop in the circuit and KCL to write equations for each node. Solve the resulting equations simultaneously to find the unknown voltages and currents.

## 4. Can KVL and KCL be applied to all types of circuits?

Yes, KVL and KCL can be applied to all types of circuits, including series, parallel, and combination circuits. They are fundamental laws of circuit analysis and can be used to solve any basic circuit problem.

## 5. Are there any limitations to using KVL and KCL in circuit analysis?

KVL and KCL are based on ideal circuit components and do not take into account factors such as resistance, capacitance, and inductance. In real-world circuits, these factors can affect the accuracy of the calculations. Additionally, KVL and KCL are only applicable in DC circuits and may not be accurate in AC circuits.

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