Question

Find the net resistance when each of the resistances are equal to each other and to 3 ohms. Please help me. ​

Answer 1

GiveN

Five resistances each of which is equal to 3 ohm.

To Find

Equivalent resistance of the combination.

ConcepT

$\boxed { \green { Series \: Combination} }$

• End to end combination of resistances is called series combination .

In this case equivalent resistance is given by

$R_{eq} = R_1 \ + R_2\ + R_3 \ + R_4$ .......

$\boxed { \green { Parallel \: Combination} }$

• When the resistors are connected across two same points.

In this case, equivalent resistance is given by

$\frac{1}{R_eq } = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} .....$

SolutioN

$R_4\:and\:R_5$ are in series and this combination will be parallel with $R_3$

Hence, equivalent resistance R` across $R_3$

${R`}$ = ${R_4} \: + \: {R_5}$

R` = 3 + 3 = 6 . This will be parallel with $R_3$

$\frac{1}{ \: \: R`` } = \frac{1}{3 \: } + \frac{1}{6} \\ \\ = > \: R`` \: = 2$

Now, $R_1 \: ,\: R_2 \:and \: R``$ will be in series . Hence, total equivalent resistance

= 3 + 3 + 2

= 8 ohm.

$\boxed{ \boxed{ \orange{ {Hence,\:equivalent\:resistance\:is\:8\:ohm} }}}$