I’ve been trying to figure out a way to solve this problem to no avail. I think it’s got to do with a voltage divider or voltage dropped. I’ve seen a number of questions on this topic but never one like this, where the value of particular resistor wasn’t given and has to be found, which also makes it difficult working out the total resistance in the circuit.
The question is asking you to apply both Kirchhoff's Voltage Law and Current Law, as well as Ohm's Law to solve.
We want to find R2. To do that we'll need to find its current, IR2 and voltage, VR2.
Besides the rest of the circuit values except for R2, they give you a key piece of information: voltage across R4 (VR4). Let's start with that.
- Use Ohm's Law to find current IR4 = VR4/R4
- Use Kirchhoff's Current Law to find current through R3 (IR3 = IR4, that is, recognize that they're the same)
- Use Ohm's Law to find voltage VR3 = IR4*R3
- Use Kirchhoff's Voltage Law to find VR2 = (VR3 + VR4).
With VR2 known, we move on to finding IR2:
- Use Ohm's Law to calculate IR1 = (VR1/R1) = [(18V - VR2)/R1]
- Use Kirchhoff's Current Law to calculate the net current through the R2 branch, as IR2 = (IR1 - IR4).
- Use Ohm's Law to calculate R2 = (IR2 / VR2).
Quick review of Kirchhoff's Laws:
- Voltage Law: Directed sum of all voltages around a closed loop is zero
(Battery [18V] is a positive value, while all the IR drops in the resistors are negative. All add up to zero.)
- Current Law: Sum of all currents flowing into and out of one node is zero
(Current through R1 into R2/R3/R4 node branches into currents out via R2 and R3+R4.)
The others have said it, but I'll list it out here in order of how I would solve it:
- Perform nodal voltage analysis - There will be two unknowns, one of them being R2, the other being V(R2).
- The voltage they gave you is important, use V = I*R to solve for I4. Because R3 and R4 are in series, the current is the same.
- You now know I4 = I3, therefore you also now know V(R3). Why is that helpful? Well, the voltage across V(R2) is in parallel with V(R3) + V(R4), otherwise, V(R2) = V(R3) + V(R4)
- Going back to the original voltage nodal equation you did in step 1, now, there is only 1 unknown, the resistance value of R2.
Try and go through the process and do the numbers, and post what you get; otherwise, comment if you get stuck.