Question

the least resistance of played by using 2 ohm, 4 ohm, 1 ohm and 100 ohm is (a) 100 ohm (b) 4 ohm (c) 1 ohm (d) 2 ohm​

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

☯ Given :

There are 4 resistors which are 2Ω, 4Ω, 1Ω, 100Ω.

$\rule{200}{1}$

☯ To Find :

We have to find the least resistance obtained by using these resistance.

$\rule{200}{1}$

☯ Solution :

Let (R1) = 1Ω, (R2) = 2Ω, (R3) = 4Ω and (R4) = 100Ω

We know that, if we will put all the resistance in paralell we can get the reaistance.

We know the case of resitance in parallel.

$\tiny{\star{\boxed{\sf{Parallel \: combination (\frac{1}{R}) = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}}}}}$

Putting Values

$\sf{\rightarrow \frac{1}{R} = \frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{100}} \\ \\ \bf{Taking \: LCM} \\ \ \ \sf{\rightarrow\frac{1}{R} = \frac{100 + 50 + 25 + 1}{100}} \\ \\ \sf{\rightarrow \frac{1}{R} = \frac{150 + 26}{100}} \\ \\ \sf{\rightarrow \frac{1}{R} = \frac{176}{100}} \\ \\ \sf{\rightarrow R = \frac{100}{176}} \\ \\ \sf{\rightarrow R = 0.56 \: Ω} \\ \\ \Large{\implies{\boxed{\boxed{\sf{R = 1 \: \Omega}}}}}$

$\therefore$ Option C is correct.

Answer 2

Answer:

Given :

There are 4 resistors which are 2Ω, 4Ω, 1Ω, 100Ω.

☯ To Find :

We have to find the least resistance obtained by using these resistance.

☯ Solution :

Let (R1) = 1Ω, (R2) = 2Ω, (R3) = 4Ω and (R4) = 100Ω

We know that, if we will put all the resistance in paralell we can get the reaistance.

We know the case of resitance in parallel.

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