Question

Calculate the equivalent resistance between points A and B:

CLASS 10th ​

Answer 1

Answer:

$\sf { \dfrac{40}{3} \Omega}$

Explanation:

Here, we are given a circuit. We need to calculate the equivalent resistance.

Before applying any formula to calculate resistance, we need to rearrange the circuit diagram. Refer to the attachment [Figure 2].

Here,

• R₁ = 5 Ω
• R₂ = 5 Ω
• R₃ = 5 Ω
• R₄ = 5 Ω
• R₅ = 5 Ω

R₁ and R₂ are connected in series combination. So, equivalent resistance of R₁ and R₂ will be,

$\longrightarrow \sf { R_{(1,2)} = R_1 + R_2 }$

$\longrightarrow \sf { R_{(1,2)} =(5 +5) \Omega}$

$\longrightarrow \sf { R_{(1,2)} =10 \Omega}$

Now, combination of R₁ and R₂ and resistance R₃ will become in parallel combination. [Figure 3]

$\longrightarrow \sf { \dfrac{1}{R_{(1,2,3)}} = \dfrac{1}{R_{1,2}} + \dfrac{1}{R_3} }$

$\longrightarrow \sf { \dfrac{1}{R_{(1,2,3)}} =\Bigg [ \dfrac{1}{10}+ \dfrac{1}{5} \Bigg] \Omega }$

$\longrightarrow \sf { \dfrac{1}{R_{(1,2,3)}} =\Bigg [ \dfrac{1 + 2}{10} \Bigg] \Omega }$

$\longrightarrow \sf { \dfrac{1}{R_{(1,2,3)}} =\Bigg [ \dfrac{3}{10} \Bigg] \Omega }$

After reciprocating both sides,

$\longrightarrow \sf { R_{(1,2,3)} = \dfrac{10}{3} \Omega }$

Now, combination of R₁,R₂ and R₃ and R₄ , R₅ will become in series combination. [Figure 4]

$\longrightarrow \sf { R_{(1,2,3,4,5)} = \Bigg [ R_{(1,2,3)} + 5 + 5 \Bigg ] \Omega }$

$\longrightarrow \sf { R_{(1,2,3,4,5)} = \Bigg [ \dfrac{10}{3} + 5 + 5 \Bigg ] \Omega }$

$\longrightarrow \sf { R_{(1,2,3,4,5)} = \Bigg [ \dfrac{10 + 15 +15}{3} \Bigg ] \Omega }$

$\longrightarrow \underline{\boxed{\sf { R_{(1,2,3,4,5)} = \dfrac{40}{3} \Omega} }} \; \bigstar$

$\therefore$ Equivalent resistance of the circuit is 40/3 Ω.