Question

find the effective resistance​

Answer 1

Answer:

6Ω

Explanation:

[ Refer to the attachment once for beter understanding. {Figure 1} :) ]

Here, we have :

• R₁ = 6 Ω
• R₂ = 6 Ω
• R₃ = 6 Ω
• R₄ = 6 Ω

Clearly, R₁ and R₂ are in parallel combination. Also, R₃ and R₄ are in parallel combination.

So, firstly we'll find the combined resistance of R₁ , R₂ and R₃ , R₄ .

Finding the combined resistance of R₁ , R₂ :

As they are in parallel combination, so equivalent resistance will be given by,

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

Substitute the values.

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

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

$\longmapsto \rm { \dfrac{1}{R_{(1,2)}} =\dfrac{2}{6} }$

On reciprocating both sides,

$\longmapsto \rm { R_{(1,2)} = \cancel{\dfrac{6}{2} }}$

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

∴ Combined resistance of R₁ and R₂ is 3 Ω.

$\rule{200}2$

Finding the combined resistance of R₃ , R₄ :

As they are in parallel combination, so equivalent resistance will be given by,

$\longmapsto \bf { \dfrac{1}{R_{(3,4)}} = \dfrac{1}{R_3} + \dfrac{1}{R_4} }$

Substitute the values.

$\longmapsto \rm { \dfrac{1}{R_{(3,4)}} = \dfrac{1}{6} + \dfrac{1}{6} }$

$\longmapsto \rm { \dfrac{1}{R_{(3,4)}} =\dfrac{1+1}{6} }$

$\longmapsto \rm { \dfrac{1}{R_{(3,4)}} =\dfrac{2}{6} }$

On reciprocating both sides,

$\longmapsto \rm { R_{(3,4)} = \cancel{\dfrac{6}{2} }}$

$\longmapsto \bf { R_{(3,4)} = 3 \; \Omega }$

∴ Combined resistance of R₃ and R₄ is 3 Ω.

$\rule{200}2$

Now, the the combined resistance of R₁ , R₂ and R₃ , R₄ will become in series combination (Figure 2 in the attachment). Equivalent resistance in series combination is given by,

$\longmapsto \rm { R_{(1,2,3,4)} = R_{(1,2)} + R_{(3,4)} }$

$\longmapsto \rm { R_{(1,2,3,4)} = (3 +3) \; \Omega }$

$\longmapsto \bf { R_{(1,2,3,4)} = 6 \; \Omega }$

∴ Effective resistance of the circuit is 6Ω.

$\rule{200}2$

Points to remember :

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

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

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

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