Question

Show how will you connect three resistors of 6ohm so that the combination has resistance of1) 18 ohm2) 2 ohm

Answer 1

Answer:

1) Connect all the three 6Ω resistors in series combination.

1) Connect all the three 6Ω resistors in parallel combination.

Explanation:

1) To get the equivalent resistance of 18 Ω :

We know that,

When resistors are connected in series combination, then equivalent resistance is given by :

$\longmapsto \bf { R_S = R_1 + R_2 + R_3+ \dots R_n }$

So, according to the diagram (in that attachment 1) :

$\longmapsto \rm { R_{(1,2,3)} = R_1 + R_2 + R_3 }$

$\longmapsto \rm { R_{(1,2,3)} = (6+6+6) \; \Omega }$

$\longmapsto \bf { R_{(1,2,3)} = 18 \; \Omega }$

∴ If we connect all the three 6Ω resistors in series combination, we'll get the equivalent resistance of 18 Ω.

2) To get the equivalent resistance of 2 Ω :

We know that,

When resistors are connected in parallel combination, then equivalent resistance is given by :

$\longmapsto \bf { \dfrac{1}{R_P} =\dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dots \dfrac{1}{R_n}}$

So, according to the diagram (in that attachment 2) :

$\longmapsto \rm { \dfrac{1}{R_{(1,2,3)}} =\dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} }$

$\longmapsto \rm { \dfrac{1}{R_{(1,2,3)}} =\Bigg ( \dfrac{1}{6} + \dfrac{1}{6} + \dfrac{1}{6} \Bigg )\; \Omega}$

$\longmapsto \rm { \dfrac{1}{R_{(1,2,3)}} =\Bigg ( \dfrac{1+1+1}{6} \Bigg )\; \Omega}$

$\longmapsto \rm { \dfrac{1}{R_{(1,2,3)}} =\Bigg ( \dfrac{3}{6} \Bigg) \; \Omega}$

On reciprocating both sides,

$\longmapsto \rm { R_{(1,2,3)}=\Bigg ( \dfrac{6}{3} \Bigg ) \; \Omega}$

$\longmapsto \bf { R_{(1,2,3)}= 2 \; \Omega}$

∴ If we connect all the three 6Ω resistors in parallel combination, we'll get the equivalent resistance of 2 Ω.

Points to remember :

• When resistors are connected in series combination, then equivalent resistance is given by :

$\longmapsto \bf { R_S = R_1 + R_2 + R_3+ \dots R_n }$

• When resistors are connected in parallel combination, then equivalent resistance is given by :

$\longmapsto \bf { \dfrac{1}{R_P} =\dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dots \dfrac{1}{R_n}}$