Question

what is the total resistance of 2 ohms, 3 ohm, 5 ohm in parallel connection ​

Answer 1

Let the total resistance be R .

$r_1=2ohm\\\\r_2=3ohm\\\\r_3=5ohm$

For parallel connection resistors formula is :

$\frac{1}{R}=\frac{1}{r_1}+ \frac{1}{r_2} +\frac{1}{r_3}$

$\frac{1}{R}=\frac{1}{2} +\frac{1}{3} +\frac{1}{5}$

$\frac{1}{R}=\frac{15+10+6}{30} \\\\\frac{1}{R} =\frac{31}{30}$

$R=\frac{30}{31}$

Hence , R = 30/31 Ω .

Answer 2

AnswEr:-

The Required Answer is 0.96 ohm (Approx).

ExplanaTion:-

Given Resistors:-

• Of Resistance 2, 3 and 5 ohm.

• All three resistors are connected in parallel.

To Find:-

• The Equivalent Resistance i.e. total resistance.

Formula Used:-

In A parallel Combination,

$\bf\longrightarrow \boxed{ \bf \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} ...... \frac{1}{R_n}}.$

Where,

• Req = Equivalent Resistance.

• R1, R2 are the given Resistors.

So Here,

• Req = ?? [to find].

• R1 = 2 ohm.

• R2 = 3 ohm.

• R3 = 5 ohm.

Now,

By putting the above values in the formula we get,

$\tt\mapsto \dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} .$

$\tt\mapsto\dfrac{1}{R_{eq}} = \bigg(\dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{5} \bigg) \: \: ohm$

$\tt\mapsto\dfrac{1}{R_{eq}} = \bigg(\dfrac{15 + 10 +6 }{30} \bigg) \: \: ohm .$

$\rm \big(by \: \: taking \: \: lcm \big).$

$\tt\mapsto\dfrac{1}{R_{eq}} = \bigg(\dfrac{31}{30} \bigg) \: ohm .$

$\tt\mapsto R_{eq} = \bigg( \dfrac{30}{31} \bigg) \: \: ohm .$

$\red{\tt\mapsto{ \boxed{ \bf R_{eq} = 0.96 \: ohm}}} \: \: \big( \rm approx \big).$

Therefore the total resistance is 0.96 ohm.