Question

what is the total resistance of a circuit consisting of a parallel combination of three resistor each of 6 ohms is connected in series with another parallel combination of two resistors of 5 ohms each?

Answer 1

In parallel combination of 3 resister of 6 ohm Rp=1/r+1/r

1/Rp=1/6+1/6+1/6

1/Rp=3/6

Rp=2

another parallel combination of two resister of 5 ohms

1/Rp=1/5+1/5

1/Rp=2/5

Rp=5/2

adding both resistenses

2+5/2

4/2+5/2

9/2 is the total resistense

Answer 2

Concept:-

It might resemble a word or a number representation of the quantity's arithmetic value. It could resemble a word or a number that represents the numerical value of the quantity.

Given:-

The given question is that consisting of a parallel combination of three resistor each of $6$ ohms is connected in series with another parallel combination of two resistors of $5$ ohms each.

Find:-

We have to find the total resistance of a circuit.

Solution:-

According to the resistance of the parallel circuit

$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

In parallel combination of $3$ resistors of $6$ ohm

$Rp=1/r+1/r+1/r\\1/Rp=1/6+1/6+1/6\\1/Rp=3/6\\Rp=2$

Another parallel combination of two resistors of $5$ ohms

$1/Rp=1/5+1/5\\1/Rp=2/5\\Rp=5/2$

Adding both resistances

$2+5/2\\4/2+5/2$

$9/2$ is the total resistance.

Hence, the total resistance of a circuit is $9/2$.

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