Question

6 ohm 8ohm 12 ohm are connected with parallel. Find the equivalent resistance

Answer 1

Answer :

$\boxed{\sf { \dfrac{8}{3} \: \Omega}}$

Given Information :

• 6Ω, 8Ω , 12Ω resistors are connected in parallel combination.

To calculate :

• Equivalent resistance (R)

Calculation :

In parallel combination , equivalent resistance of the circuit is given by the formula,

$\boxed {\sf{ \dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dots \dfrac{1}{R_n}} }$

Here,

• $\rm {R_1 = 6 \Omega }$

• $\rm {R_2 = 8 \Omega }$

• $\rm {R_3 = 12 \Omega }$

Substituting values,

$\longrightarrow \sf { \dfrac{1}{R_p} = \left \lgroup \dfrac{1}{6} + \dfrac{1}{8} + \dfrac{1}{12} \right \rgroup \: \Omega}$

$\longrightarrow \sf { \dfrac{1}{R_p} = \left \lgroup \dfrac{4 + 3 + 2}{24} \right \rgroup \: \Omega}$

$\longrightarrow \sf { \dfrac{1}{R_p} = \left \lgroup \dfrac{9}{24} \right \rgroup \: \Omega}$

$\longrightarrow \sf { \dfrac{1}{R_p} = \left \lgroup \dfrac{3}{8} \right \rgroup \: \Omega}$

After reciprocation,

$\longrightarrow \sf \red{ R_p = \dfrac{8}{3} \: \Omega}$

Therefore, equivalent resistance of the circuit is $\sf { \dfrac{8}{3} \: \Omega}$.

Points to remember :

In parallel combination , equivalent resistance of the circuit is given by the formula,

$\longmapsto \boxed {\sf{ \dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dots \dfrac{1}{R_n}} }$

In series combination , equivalent resistance of the circuit is given by the formula,

$\longmapsto \boxed {\sf{ R_s = R_1 + R_2 + R_3 + \dots R_n} }$