Question

equivalent resistance between points a and b if R=60 ohms?

Answer 1

This seems complicated but it's actually really easy!

What you have here are "three" resistors in PARALLEL. I use the quotes because each of the "three" resistors is made of several resistors in SERIES that contribute to the equivalent resistance of each "resistor" in parallel. All you need to do is make sure you add the resistances properly to get the appropriate equivalent resistance, R(eq).

For resistors in series:
\[R_{eq}=R_1+R_2+R_3+...\]
For resistors in parallel:
\[{1 \over R_{eq}}={1 \over R_1}+{1 \over R_2}+{1 \over R_3}+...\]
Let's say each row in the circuit contains "one" resistor. That gives us 3 resistors in parallel, so the equation for equivalent resistance will be:
\[{1 \over R_{eq}}={1 \over R_{top}}+{1 \over R_{middle}}+{1 \over R_{bottom}}\]
Now we need to consider that that top and middle rows have several resistors in series. This means:
\[R_{top}=R+R+R=3R\]\[R_{middle}=R+R=2R\]\[R_{bottom}=R\]
We can sub these into our original equation to find R(eq) of the circuit:
\[{1 \over R_{eq}}={1 \over 3R}+{1 \over 2R}+{1 \over R}\]
Since R=60 ohms, you should be able to solve for R(eq) pretty easily now! Let me know what your answer is and if you have any questions!

Answer 2

32.7 ohms. thanks for the help!

Answer 3

Looks good! And no problem!