Question

What is the
is the minimum resistance which can
be made using five resistons each of 1/2ohm?​

Answer 1

Answer:

We have 5 resistors each with resistance of 1/2 ohm.

Minimum resistance means that the resistors are connected in parallel connection.

Hence, 1/R' = 1/R1 + 1/R2....+ 1/Rn

Now,

➸ 1/R' = 1/½ + 1/½ + 1/½ + 1/½ + 1/½

➸ 1/R' = 5*(1/½)

➸ 1/R' = 5*(1*2/1)

➸ 1/R' = 5*2

➸ 1/R' = 10

➸ R' = 1/10

➸ New resistance = 0.1 ohm

So, the minimum net resistance of the circuit is 0.1 ohm.

Let also find the maximum net resistance of the circuit.

R' = R1 + R2 .... + Rn

➸ R' = ½ + ½ + ½ + ½ + ½

➸ R' = 5/2

➸ R' = 2.5 ohm

Answer 2

$\green{ Given}$

• Five resistors each of $\frac{1}{2}$ ohm.

$\green{To \:Find}$

• Minimum resistance that can be obtained using five such resistors.

$\green{Concept}$

• When a number of resistors are connected In series, we get the maximum resistance.Let this resistance be $R_1$

• When a number of resistors are connected In parallel, we get the minimum resistance.Let this resistance be $R_2$

• When a number of resistors are connected in both series and some in parallel we get resistance between $R_1$ and $R_2$

$\green{Solutions}$

Hence, minimum resistance will be obtained in case of parallel combination.

In case of parallel combination ,

$R_{eq} = \frac{1}{ R_ 1} + \frac{1}{ R_2 } + \frac{1}{ R_3} \: and \: so \: on$

Here, each resistance is R , hence Req will be

$R_{eq} = \frac{1}{ 0.5} + \frac{1}{ 0.5 } + \frac{1}{0.5} + \frac{1}{0.5} + \frac{1}{0.5 } \\ \\ \\ = > R_{eq} = \frac{5}{0.5} \\ \\ \\ = > R_{eq} = 0.1 \: ohm$

$\boxed{ \: \pink{hence ,\: the \: minimum \: resistance \: is \: 0.1 \: ohm \: } \: }$