Problem 78.
What is the equivalent resistance between points A and B?
Solution
To find the current through the battery, we need to find the equivalent resistance of the circuit. With the known equivalent resistance of the circuit, the current is
Thus the first step is to find the equivalent resistance of the circuit.
We can clearly see (figure below) that two 20 ohm resistors are connected in parallel (red line), two 10 ohm resistors are connected in series (green line), three 20 ohm resistors are connected in series (blue line).
We can find the corresponding equivalent resistances:
 two 20 ohm resistors connected in parallel:
 two 10 ohm resistors connected in series:
 three 20 ohm resistors connected in series:
Now we have a circuit shown in the figure below. In this circuit two 10 ohm resistors are connected in series. We replace them with an equivalent resistor with the resistance of
Now we have two 20 ohm resistors connected in parallel (see figure below). We replace them with in an equivalent resistance of
In the equivalent circuit we have two 10 ohm resistors connected in series (see figure below). We replace them with an equivalent resistance of
Finally we have 20 ohm and 60 ohm resistors connected in parallel (see figure below), which can be replaced with an equivalent resistance of
Then two resistors (30 ohm and 15 ohm) are connected in series. Their equivalent resistance, which is equivalent resistance of the whole circuit, is
Now we can find the current through the battery, which is
