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GUJCET · Physics · Current Electricity
What is the equivalent resistance between A and B in the given circuit ?
- A \(\frac{3}{8} \Omega\)
- B \(\frac{8}{3} \Omega\)
- C \(2 \Omega\)
- D \(4 \Omega\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{3} \Omega\)
Step-by-step Solution
Detailed explanation
(B)
equivalent resistance between AC and CD
\(R_1=2+2=4 \Omega\)
equivalent resistance between \(R_1\) and AD
\({l}\frac{1}{ R _2}=\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2} \\ R _2=2 \Omega\)
equivalent resistance between \(R_2\) and DE
\(R_3=2+2=4 \Omega\)
equivalent resistance between \(R_3\) and AE
\({l}\frac{1}{R_4}=\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2} \\ R_4=2 \Omega\)
equivalent resistance between \(R_4\) and EB
\(R _5=2+2=4 \Omega\)
equivalent resistance between \(R_5\) and AB
\({l}\frac{1}{R_{A B}}=\frac{1}{4}+\frac{1}{8}=\frac{2+1}{8}=\frac{3}{8} \\ \therefore R_{A B}=\frac{8}{3} \Omega\)
equivalent resistance between AC and CD
\(R_1=2+2=4 \Omega\)
equivalent resistance between \(R_1\) and AD
\({l}\frac{1}{ R _2}=\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2} \\ R _2=2 \Omega\)
equivalent resistance between \(R_2\) and DE
\(R_3=2+2=4 \Omega\)
equivalent resistance between \(R_3\) and AE
\({l}\frac{1}{R_4}=\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2} \\ R_4=2 \Omega\)
equivalent resistance between \(R_4\) and EB
\(R _5=2+2=4 \Omega\)
equivalent resistance between \(R_5\) and AB
\({l}\frac{1}{R_{A B}}=\frac{1}{4}+\frac{1}{8}=\frac{2+1}{8}=\frac{3}{8} \\ \therefore R_{A B}=\frac{8}{3} \Omega\)
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