Question

calculate the equivalent resistance between two points A and b in the circuit shown in figure​

Answer 1

Answer:

Let's assume current enters the circuit from 'A'. Now it has two ways to flow through. One way is to flow through 6 ohm resistor and other is flow through 8 ohm resistor.

Based on the Current division rule, it will get divided and flow through both the resistors. Now the current flowing through 8 will flow through 9 ohm resistor and then via 7 ohm resistor to reach B.

On the other hand, the current flowing through 6 ohms directly reaches point B. Hence now both these currents merge at B and add up to the original current (current present before getting divided at A.)

Now there might be a confusion on how to check whether a resistor is in series or parallel connection. To confirm whether the combination is series or parallel, check whether the current is getting divided or not.

Taking this example, we see current gets divided at A. Hence both the resistors connected at Point A are in parallel. But we can see that, 8 ohm, 9 ohm and 7 ohm have the same current flowing through them without any division. Hence they are in series.

Now again, at B both these currents get added at the intersection. Hence 6 and 7 ohms are also in parallel. On closer look, we see that:

• 8,9,7 ohm resistors are in series.

⇒ Net resistance = 8 + 9 + 7 = 24 ohms.

• 6 ohm and 24 ohms are in parallel connection.

⇒ Effective Resistance:

$\implies \dfrac{1}{R} = \dfrac{1}{6} + \dfrac{1}{24}\\\\\\\implies \dfrac{1}{R} = \dfrac{4+1}{24} = \dfrac{5}{24}\\\\\\\implies R = \dfrac{24}{5} = 4.8 \:\Omega$

Hence the final and the required answer is 4.8 ohms.