Kirchoff's law

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conage
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Joined: Mon Jul 23, 2018 5:38 am

Kirchoff's law

Post by conage » Mon Jul 23, 2018 5:50 am

I was having trouble uploading an image but I think it's okay now. The question is:

Calculate the current in the circuit of Fig. 19-53, and show that the sum of all the voltage changes around the circuit is zero.

Image

I know we have to use kirchoff's law and we have one loop on the inside. How do we know where to put i1 and I2?

jeff
Site Admin
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

Re: Kirchoff's law

Post by jeff » Mon Jul 23, 2018 1:27 pm

Hi conage,
conage wrote:
Mon Jul 23, 2018 5:50 am
I was having trouble uploading an image but I think it's okay now. The question is:

Calculate the current in the circuit of Fig. 19-53, and show that the sum of all the voltage changes around the circuit is zero.

Image

I know we have to use kirchoff's law and we have one loop on the inside. How do we know where to put i1 and I2?
Let me answer your question first. Since this circuit has a single loop, the current does not branch off anywhere and so the current is the same everywhere in the circuit. So to use Kirchoff's Laws for this circuit, you would only have one current i.

However, I don't believe they actually want you to use Kirchoff's voltage law for this one. They want you to show that the sum of the voltage changes is zero, but that's the starting point for the Voltage Law.

(In other words, this problem is not about using Kirchoff's law, it's about proving that it works in this case.)

So here's what I would suggest, since these resistors are all in series:
  • combine these series resistors into one equivalent resistor
  • use the equivalent resistance and the battery voltage in Ohm's Law to find the total current
  • for each resistor, use Ohm's law and the total current to find the voltage drop across each resistor
  • show that the voltage drops add up to the battery voltage
Of course, this is all really equivalent to using Kirchoff's laws! But the point is, when we use the KVL around a loop we set the total voltage change to zero, while this problem is asking us to show that it is zero.

I hope this helps! Let me know if you have more questions or would like me to check your results.

conage
Posts: 2
Joined: Mon Jul 23, 2018 5:38 am

Re: Kirchoff's law

Post by conage » Mon Jul 23, 2018 3:51 pm

okay I got .35

thank you for your help

jeff
Site Admin
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

Re: Kirchoff's law

Post by jeff » Mon Jul 23, 2018 4:00 pm

conage wrote:
Mon Jul 23, 2018 3:51 pm
okay I got .35

thank you for your help
That's right, the current is 0.35 A (or 0.353 A if we keep an extra digit).

Now if you use that and Ohm's law for each individual resistor:

V = I R = (0.353 A) (2 ohms) = 0.71 V
V = I R = (0.353 A) (14 ohms) = 4.94 V
V = I R = (0.353 A) (9.5 ohms) = 3.35 V

Those are the voltage drops for each resistor, and if you add them up you get 9 V.

So the total voltage drop across the resistors is 9 V, and the voltage rise is 9 V from the battery, and therefore the total voltage change going all around the loop is zero.

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