CBSE 2025 · Region 2 · Set 1 · Q32 · 3 marks
Three resistors of $\displaystyle 2 \Omega, 3 \Omega$ and $\displaystyle 6 \Omega$ are connected in (i) series, and(ii)parallel. Draw the arrangements of the resistors and find the equivalent resistance of each arrangement.
Three resistors of $\displaystyle 2 \Omega, 3 \Omega$ and $\displaystyle 6 \Omega$ are connected in (i) series, and
(ii)
parallel. Draw the arrangements of the resistors and find the equivalent resistance of each arrangement.
Marking-scheme solution
(i)
In series, \(\displaystyle \mathrm{R}_{\mathrm{s}}=\mathrm{R}_{1}+\mathrm{R}_{2}+\mathrm{R}_{3}\)
\[=(2+3+6) \Omega=11 \Omega
\]
(ii)
In parallel,
\[\begin{aligned}
\frac{1}{R_{p}} & =\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \\
& =\frac{1}{2}+\frac{1}{3}+\frac{1}{6} \\
& =\frac{3+2+1}{6} \\
& R_{p}=1 \cdot 0 \Omega
\end{aligned}
\]
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