#### Question

Calculate the combined resistance in each case:

#### Solution

case 1

Let the total resistance of the combination shown in the diagram below be *R*.

Here 500 Ω and 1000 Ω resistors are connected in series combination. Their net resistance is given by *R *= *R*_{1}+ *R*_{2}

Here:*R*_{1}=500 Ω*R*_{2}=1000 Ω

So:*R* = 500 + 1000 = 1500 Ω

Thus, the total resistance of the combination is 1500 Ω.

case 2

In the circuit diagram shown above, two 2 â„¦ resistors are connected in parallel combination.

Therefore:

`1/R_-p=1/R_1+1/R_2`

`1/R_p=1/2+1/2`

`Ω1/R_p=2/2=1`Ω

Thus the total resistance of the combination is 1 Ω.

case 3

In the circuit diagram shown above, two 4 â„¦ resistors are connected in parallel combination.

Therefore their resulant resistance given by

`1/R=1/R1+1/R_2`

`Here R_1=4`Ω

`R_2=4`Ω

So

`1/R=1/4+1/4`

`or 1/R=2/4`

or R=2Ω

In the above circuit diagram, this 2 â„¦ and 3 â„¦ resistors are connected in series combination. So, the total resistance of the circuit can be calculated as:

`R=R_1+R_2`

Here

`R_1=2`â

`R_2=3`â

So:

R=2â+3â=5â

Thus, the total resistance of the combination is 5 â„