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GUJCET · Physics · Current Electricity
As shown in the figure, balanced condition of Wheatstone Bridge is \(n=\) ___________ .
- A \(\frac{3}{2}\)
- B \(\frac{2}{5}\)
- C \(\frac{1}{2}\)
- D \(\frac{5}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
From the figure:
- \(R_1=15 \Omega\)
- \(R_2=10 \Omega\)
- \(R_3=5 \Omega\)
- \(R_4=\) equivalent resistance of the right branch.
\(\begin{array}{l}\text { - } 2 \Omega \\ \text { - } n \Omega\end{array}\)
\(R_4=\frac{2 n}{2+n}\)
\(\frac{15}{10}=\frac{5}{\frac{2 n}{2+n}}\)
\(\frac{3}{2}=\frac{5(2+n)}{2 n}\)
Multiply both sides by \(2 n\) :
\(\begin{array}{c}3 n=5(2+n) \\3 n=10+5 n \\2 n=10 \\n=\frac{1}{2}\end{array}\)
- \(R_1=15 \Omega\)
- \(R_2=10 \Omega\)
- \(R_3=5 \Omega\)
- \(R_4=\) equivalent resistance of the right branch.
\(\begin{array}{l}\text { - } 2 \Omega \\ \text { - } n \Omega\end{array}\)
\(R_4=\frac{2 n}{2+n}\)
\(\frac{15}{10}=\frac{5}{\frac{2 n}{2+n}}\)
\(\frac{3}{2}=\frac{5(2+n)}{2 n}\)
Multiply both sides by \(2 n\) :
\(\begin{array}{c}3 n=5(2+n) \\3 n=10+5 n \\2 n=10 \\n=\frac{1}{2}\end{array}\)
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