# Calculate resistance using Kirchoff's laws

#### Arans9

Joined Dec 15, 2018
3
Hi all!

Upon my first attempt i thought this wasn't too hard and i got an answer. Unfortunately it turns out that i used Ohms law instead of Kirchoff's laws.

I've been trying to solve this for a long time now, but i just can't do it as it doesn't have any information about the current or total resistance.

I think that voltage could be the same across each component of the parallel circuit. So the voltage across the 5 ohms resistor could be 75 Volts

Your help is greatly appreciated, thank you.

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#### dl324

Joined Mar 30, 2015
11,317
Welcome to AAC!

You have to use both laws. Post your work and the complete text of the problem.

#### WBahn

Joined Mar 31, 2012
26,074
We can only tell you what you are doing wrong (or right) to the degree that you show us what you are doing.

Yes, the 75 Ω and 5 Ω resistors are in parallel and so they have the same voltage across them. What does this tell you about the currents in at least some of the branches?

#### ebp

Joined Feb 8, 2018
2,332
You can do it without using Ohm's law as such, though there is no way to do it without the underlying concept of Ohm's law. Consider "proprtionality."

While you may think you solved it using only Ohm's law, in reality you have applied Kirchhoff's as well, but I think you didn't realize you were doing it. I suggest re-examining your process using Ohm's law and think about how you arrived at the values you needed to get to the solution.

#### Arans9

Joined Dec 15, 2018
3
Ok guys thank for your responses!

This is my crack at it!

#### BBee

Joined Dec 6, 2018
35
That looks good! The only thing I would point out is that on some courses giving an answer in that form without clearly stating what it is (even though right) may upset some lecturers. Following from this you could explicity show the equations for the sum of the voltages etc

Obviously you have to work to the course you are on, but I agree, from experience, that in practice one uses Ohm's, Kirchoff's and Norton's (like Kirchoff's but with current as the subject) laws interchangeably, as 'ebp' mentioned above, without concious thought, to get to a result.

Tracy

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#### BBee

Joined Dec 6, 2018
35
As an addition, as I am not totally sure what would be required, with a bit of work using the resultant value of the 20 and 5 ohm, it is possible to determine the value of the unknown resistor without reference to current at all using algebra and a bit of substitution. See : https://www.electronics-tutorials.ws/dccircuits/kirchhoffs-voltage-law.html

It will be possible to do this using the original resistors values from scratch but the maths will get fiddly.

Tracy

#### ebp

Joined Feb 8, 2018
2,332
Here's what I meant by "proportionality"

(the parallel combination of the 5 and 20 ohm resistors is treated as a single 4 ohm)
The voltage across 4 ohms is 75 V (specified & using KVL)
The voltage across the unknown resistor is 125 V (KVL)
The current through the unknown resistor is the same as through the 4 ohm resistor (KCL)
The value of the unknown resistance is
125V / 75V x 4 ohms = 6.67 ohms (proportionality, with no need to actually quantify the current)

#### Arans9

Joined Dec 15, 2018
3
Thank you so much!! That's very interesting Tracy what you did there. Does this 'proportionality' concept have any to do with superposition?

Unfortunately I don't have much experience with electrical circuit theory and so while I can explain it in person using words, I find it very difficult to present it in a 'model answer' format. Kirchoff's laws are especially tricky .

#### dl324

Joined Mar 30, 2015
11,317
Kirchoff's laws are especially tricky .
They're just addition or subtraction. Nothing very tricky.

#### WBahn

Joined Mar 31, 2012
26,074
Thank you so much!! That's very interesting Tracy what you did there. Does this 'proportionality' concept have any to do with superposition?

Unfortunately I don't have much experience with electrical circuit theory and so while I can explain it in person using words, I find it very difficult to present it in a 'model answer' format. Kirchoff's laws are especially tricky .
Kirchhoff's Laws are easy to understand and apply if you understand the underlying principles involved.

Imagine being in the mountains standing at Point A. You now travel to Point B which 300 ft higher than Point B. Then you travel to Point C which is 400 ft lower than Point B. Is Point C higher or lower than Point A and by how much?

This is nothing more than Kirchhoff's Voltage Law applied to gravitational potential energy and saying that the sum of elevation gains around any closed loop must be zero. Well, voltage is a measure of electrical potential energy on a per unit charge basis just like elevation is a measure of gravitational potential energy on a per unit mass basis. So the sum of voltage gains around any closed loop must be zero.

Kirchhoff's Current Law is even more understandable in everyday terms -- what goes in must come out. The sum of the current flowing into a node must equal the sum of the currents flowing out of a node.