Question

find the total resistance of the following circuit in which r1=3ohm r2= 3ohm r3= 4ohm r4= 2ohm

Answer 1

AnsWer :

3 Ohm.

Concepts Required :

• Series Combination - series combination define as When Current follow only one path in whole Circuit and not change there direction, it said to be Series Combination.
• Rs - R1 + R2 + R3... Rn.

• Parellel Combination - parellel Combination define as When Current follow two or more path in there Circuit and and change there direction, it said to be Parallel Combination.
• Rp - 1/R1 + 1/R2 + 1/R3...1/Rn.

Formula :

# Series Connection.

$\tt \dagger \: \: \: \: \: R_s = R_1 + R_2 + R_3 ... R_n$

# Parellel Connection.

$\tt \dagger \: \: \: \: \:\dfrac{1}{ R_P}= \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} ... \dfrac{1}{R_n}$

Solution :

We have,

• A Circuit in which R1 , R2 , R3 and R4 are connect through it.

Let,

• Current be ( I )

A/Q,

• R1 and R2 are Connected in Series Combination. ( Path - 1 )
• And, R3 and R4 are also connected in Series Combination. ( path -2 )
• And, When Current ( I ) flow in the circuit the Current divided/ follow into two different path ( path 1 & path 2 )

So,

Taking Path 1.

$\tt \dagger \: \: \: \: \: R_s = R_1 + R_2 + R_3 ... R_n$

Where as,

• R1 = 3 ohm.
• R2 = 3 ohm.
• R3 = 4 ohm.
• R4 = 2 ohm.

$\tt\longmapsto R_s = R_1 + R_2.$

$\tt \longmapsto R_s = 3 + 3.$

$\tt \longmapsto R_s = 6\Omega .$

$\rule{90}1$

Taking Path 2.

$\tt \longmapsto R_s = R_3 + R_4.$

$\tt \longmapsto R_s = 4 + 2.$

$\tt \longmapsto R_s = 6\Omega .$

$\rule{90}1$

Now,

• Path 1 & 2 follow Parellel combination.

Let,

• Rs1 = 6 ohm. ( Path 1 )
• Rs2 = 6 ohm. ( Path 2 )

$\tt \dagger \: \: \: \: \:\dfrac{1}{ R_P}= \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} ... \dfrac{1}{R_n}$

$\tt \longmapsto \dfrac{1}{ R_P}=\dfrac{1}{ 6} + \dfrac{1}{ 6}$

$\tt\longmapsto \dfrac{1}{ R_P}=\dfrac{1 + 1}{ 6}$

$\tt\longmapsto \dfrac{1}{ R_P}=\dfrac{2 }{ 6}$

$\tt\longmapsto \dfrac{1}{ R_P}=\dfrac{1}{3}$

$\tt\longmapsto R_P =3\Omega .$

Therefore, the total Equivalent Resistance is 3 ohm.