Question

The minimum resistance that you can obtain from the given three resistors, each of resistance 12 ohm. ... *

2 points

12 ohm

1/4 ohm

4 ohm

36 ohm


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Answer 1

Question

The minimum resistance that you can obtain from the given three resistors, each of resistance 12 ohm.

a) 12 ohm

b) 1/4 ohm

c) 4 ohm

d) 36 ohm

Solution -

Given that, there are three resistors and resistance of each three resistor is 12 ohm.

We have to find the minimum resistance that can obtain from the given three resistors.

Since, there are two ways to find the resistance. One is in series and other is in parallel.

For series:

Rs = R1 + R2 + R3

Rs = 12 + 12 + 12

Rs = 36 ohm

For Parallel:

1/Rp = 1/R1 + 1/R2 + 1/R3

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

1/Rp = (1 + 1 + 1)/12

1/Rp = 3/12

1/Rp = 1/4

Rp = 4 ohm

If we compare the effective resistance of series resistance and parallel resistance then we find that the, combination which are in parallel have the minimum resistance that you can obtain from the given three resistors, each of resistance 12 ohm.

Therefore, option c) 4 ohm is the answer.

Answer 2

✪ GIVEN ✪

Three resistors each of resistance 12 Ω each.

✪ TO FIND ✪

The minimum resistance that can be obtained from the 3 resistors.

✪ FORMULAE TO BE USED ✪

For connection in series,

$\rm{R_{Equivalent}=R_1+R_2+R_3+....+R_n}$

For connection in parallel,

$\displaystyle{\rm{\frac{1}{R_{Equivalent}}=\frac{1}{R_1} +\frac{1}{R_2} +\frac{1}{R_3}+.....+\frac{1}{R_n} }}$

✪ SOLUTION ✪

Checking the equivalent resistance for all the connections :-

For connection in series,

$\rm{R_{Equivalent}=R_1+R_2+R_3}$

$\rm{\longmapsto R_{Equivalent}=12+12+12}\\\\\rm{\longmapsto R_{Equivalent}=36\ \Omega}$

$\rule{130}{2}$

For connection in parallel,

$\displaystyle{\rm{\frac{1}{R_{Equivalent}}=\frac{1}{R_1} +\frac{1}{R_2} +\frac{1}{R_3} }}$

$\displaystyle{\rm{\longmapsto \frac{1}{R_{Equivalent}}=\frac{1}{R_1} +\frac{1}{R_2} +\frac{1}{R_3} }}\\\\\\\displaystyle{\rm{\longmapsto \frac{1}{R_{Equivalent}}=\frac{1}{12} +\frac{1}{12} +\frac{1}{12} }}\\\\\\\displaystyle{\longmapsto \rm{\frac{1}{R_{Equivalent}}=\frac{3}{12} }}\\\\\\\displaystyle{\rm{\longmapsto \frac{1}{R_{Equivalent}}=\frac{1}{4} }}\\\\\\\boxed{\displaystyle{\rm{\longmapsto R_{Equivalent}=4\ \Omega}}}$

Therefore, the least resistance that can be obtained  from the 3 resistors each of 12 Ω is (C) 4 Ω.