# Trouble finding the R(equivalent) in this circuit

I started studying Electric Circuits one week ago so this material is new to me. I was trying to solve this problem from the book but I had some difficulty:

My analysis:

The equivalent resistance R1 for parallel resistors 16Ω and 48Ω is 12Ω (16x48/16+48).

The equivalent resistance R2 for parallel resistors 24Ω and 12Ω is (24x12/24+12).

The equivalent resistance R3 for resistors in series R2 and 22Ω is 30Ω (8+22).

The equivalent resistance R4 for parallel resistors R3 and 45Ω is 18Ω (30x45/30+45).

The equivalent resistance Rab for resistors in series R1 and 18Ω is 30Ω (12+18).

Why is the final answer 34Ω? Mine got 30Ω.

• Looks like a text book mistake. Happens more often then you'd like. I agree with your analysis. – ACD Sep 11 '14 at 13:57
• I got 30 Ω too. Perhaps the book is wrong! – Xcodo Sep 11 '14 at 13:58

Your book is wrong, and you are right:

simulate this circuit – Schematic created using CircuitLab

Try to simulate that, and you will get that the voltage across the current generator is 30V, i.e. the resistance seen by the current generator is $\frac{30}{1}\Omega=30\Omega$.

This trick is very useful when you have tons of exercises with no solution, plus you learn how to use a simulator (use some spice flavour). Of course you should always solve the exercise by hand and, if you are not sure your result is correct, check it with the simulator. Learning how to deal with circuits without the help of a computer is a necessary base for an EE, don't be too attracted by the simulator.

• Great idea putting a current generator and simulating using a software. I'm currently learning PSpice. – Shougo Makishima Sep 11 '14 at 14:11
• I used to do that all the times when I was studying for my circuit analysis test. Of course we used phasors so it was a bit trickier but the simulator helped tremendously. – Vladimir Cravero Sep 11 '14 at 14:13
• Yes - circuit simulation can be a very helpful tool. But also for this task? I doubt if it makes really sense. What did the user learn? Nothing. He is using Ohms law, nothing else. And that`s a great idea? During hand calculation he could learn much more: How to handle series and parallel combinations and how to jump between resistors and conductances. – LvW Sep 11 '14 at 20:54
• I thought it was clear that the simulator in this case should be used only to check the result(s), rigorously calculated by hand. Thanks for pointing that out @LvW I'm adding a few lines to the answer. – Vladimir Cravero Sep 11 '14 at 20:58
• OK - agreed. In general, I think we never should blindly rely on simulation results. It is always good to have in advance a rough idea how simulation results should look like. – LvW Sep 12 '14 at 11:00

The correct answer is $30 \Omega$:

$$R_{eq} = \dfrac{16\cdot 48}{16 + 48} + \dfrac{\left(\dfrac{24\cdot 12}{24 + 12} + 22\right)\cdot 45}{\left(\dfrac{24\cdot 12}{24 + 12} + 22\right)+45}$$ $$R_{eq} = 12 + \dfrac{(8+22)\cdot 45}{(8+22)+45}$$ $$R_{eq} = 12 + \dfrac{30\cdot 45}{30 + 45}$$ $$R_{eq} = 12 + 18 = 30$$