(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find [tex]R_2[/tex] in the circuit below.

2. Relevant equations

Kirchoff's Current Law:

[tex]\sum {I_{IN} } = \sum {I_{OUT} }[/tex]

Kirchoff's Voltage Law:

[tex]\sum {V = 0}[/tex]

3. The attempt at a solution

Using KCL for the node joining the 8ohm resistor, R2 and the 1 ohm resistor:

[tex]i_1 = i_2 + 2[/tex]

Now using KVL for the shortest route down the 1 ohm resistor from the voltage source.

[tex] - 10 + 8i_1 + 2 = 0\; \Rightarrow \;i_1 = 1\;A[/tex]

From the first equation;

[tex]i_2 = i_1 - 2 = 1 - 2 = - 1\;A[/tex]

Until this point, everything seems logical, and I think it is right.

Now in order to solve for [tex]R_2[/tex] I must now use [tex]V = IR[/tex] 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 [tex]R_2 = \frac{2}{{ - 1}} = - 2\;\Omega[/tex].

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.

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# Basic Circuit Problems - KVL and KCL

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