Question

sukruth has n number of 12 ohm resistor. how many resistor are to be connected in the circuit to get total resistor of 2 ohm .also suggest him the method of connecting the resistor, with suitable reason ​

Answer 1

Answer:

Sukruth has 12 ohm resistor.

Since n number of resistors have to be connected in the circuit to get a total equivalent resistance of 2 ohm, we have to connect the n number of 12 ohm resistors in parallel.

Explanation:

$\frac{1}{12} + \frac{1}{12} + \frac{1}{12} ..... = \frac{1}{2}$

We have n number of resistors.

Since we have to connect them in parallel, the equivalent resistance is:

$\frac{1}{12} \times n = \frac{1}{2}$

n = 6

Hence, 6 resistors of 12 ohm resistance have to be connected in parallel connection in order to get an equivalent resistance of 2 ohm

Answer 2

There are total n resistors each of resistance 12 resistance are connected in such a way that their total resistance is 2 ohm.

As the resultant resistance is minimum. So, connect them in parallel.

For parallel combination:

1/Rp = 1/R1 + 1/R2

As, there are n resistors. So,

1/Rp = 1/R1 + 1/R2 + ......... n

1/Rp = 1/12 + 1/12 + .......... n

As, the total resistance is 2 ohm. So, Rp = 2 ohm

1/2 = 1/12 + 1/12 + .......... n

1/2 = 1/12 × n

12/2 = n

6 = n

Therefore, there are total 6 resistors each having resistance 12 ohm and it's resultant is 2 ohm.

Verification

1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5 + 1/R6

As the value of each resistance is 12 ohm. So,

1/Rp = 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

1/Rp = 6/12

1/Rp = 1/2

Rp = 2 ohm