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Science · 2022 · 4 marks
CBSE 2022 · Region 3 · Set 3 · Q14
Study the following electric circuit in which the resistors are arranged in three arms A, B and C: (a) Find the equivalent resistance of arm C. (b)…
Study the following electric circuit in which the resistors are arranged in three arms A, B and C:
(a)
Find the equivalent resistance of arm C.
(b)
Calculate the equivalent resistance of the parallel combination of the arms B and C.
(c)
(i)
Determine the current that flows through the ammeter.
OR
(ii)
Determine the current that flows in the ammeter when the arm B is withdrawn from the circuit.
Marking-scheme solution
(a) \(\displaystyle R=R_{1}+R_{2}+R_{3}\)
\[\begin{aligned}
& =10 \Omega+20 \Omega+30 \Omega \\
& =60 \Omega
\end{aligned}
\]
(b) \(\displaystyle \frac{1}{R p}=\frac{1}{R_{B}}+\frac{1}{R_{C}}\)
\[\begin{aligned}
& \frac{1}{R p}=\frac{1}{30 \Omega}+\frac{1}{60 \Omega} \\
& \mathrm{R}_{\mathrm{p}}=20 \Omega
\end{aligned}
\]
(c)
(i)
\(\displaystyle R=R_{s}+R_{p}\)
\[\begin{aligned}
& =40 \Omega+20 \Omega=60 \Omega \\
& \therefore I=\frac{V}{R}=\frac{6 V}{60 \Omega}=\frac{1}{10} A=0.1 A
\end{aligned}
\]
OR
(ii)
\[\begin{gathered}
\text { Resistance }, R=40 \Omega+60 \Omega=100 \Omega \\
\therefore I=\frac{V}{R}=\frac{6 \mathrm{~V}}{100 \Omega}=0.06 \mathrm{~A}
\end{gathered}
\]
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