Question

find equivalent resistance of circuit in which two resistor of 1and 2ohm connected in series one in parallel of 3 ohm and another 2and1 ohm resistor in series​

Answer 1

Answer:

1Ω

Explanation:

[ Kindly refer to attachment for better understanding. :) ]

Here,

• $\rm R_1$ = 2Ω
• $\rm R_2$ = 1Ω
• $\rm R_3$ = 1Ω
• $\rm R_4$ = 2Ω
• $\rm R_5$ = 3Ω

Since, $\rm R_1$ and $\rm R_2$ are in series combination, so let's find the combined resistance of $\rm R_1$ and $\rm R_2$.

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

$\\ \longrightarrow \quad \sf { R_S = R_1 + R_2+\dots R_n}$

$\\ \longrightarrow \quad \sf { R_{(1,2)} = (2+1) \; \Omega}$

$\\ \longrightarrow \quad \bf\underline { R_{(1,2)} = 3 \; \Omega}$

Similarly, Since, $\rm R_3$ and $\rm R_4$ are in series combination, so let's find the combined resistance of $\rm R_3$ and $\rm R_4$.

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

$\\ \longrightarrow \quad \sf { R_S = R_1 + R_2+\dots R_n}$

$\\ \longrightarrow \quad \sf { R_{(3,4)} = (2+1) \; \Omega}$

$\\ \longrightarrow \quad \bf\underline { R_{(3,4)} = 3 \; \Omega}$

Now, the combined resistance of $\rm R_1$ and $\rm R_2$ ; $\rm R_3$ and $\rm R_4$ and $\rm R_5$ will become in parallel combination. (Fig 3)

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

$\\ \longrightarrow \quad \sf { \dfrac{1}{R_P} = \dfrac{1}{R_1} + \dfrac{1}{R_2}+\dots \dfrac{1}{R_n}}$

$\\ \longrightarrow \quad \sf { \dfrac{1}{R_{(1,2,3,4,5)}} = \dfrac{1}{R_{(1,2)}} + \dfrac{1}{R_{(3,4)}}+\dfrac{1}{R_5}}$

$\\ \longrightarrow \quad \sf { \dfrac{1}{R_{(1,2,3,4,5)}} = \dfrac{1}{3} + \dfrac{1}{3}+\dfrac{1}{3} }$

$\\ \longrightarrow \quad \sf { \dfrac{1}{R_{(1,2,3,4,5)}} = \dfrac{1+1+1}{3} }$

$\\ \longrightarrow \quad \sf { \dfrac{1}{R_{(1,2,3,4,5)}} = \dfrac{3}{3} }$

On reciprocating both sides,

$\\ \longrightarrow \quad \sf { R_{(1,2,3,4,5)} = \dfrac{3}{3} }$

$\\ \longrightarrow \quad \sf { R_{(1,2,3,4,5)} = 1\; \Omega }$

Therefore, equivalent resistance of circuit is 1Ω.