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Physics · 2026 · 3 marks
CBSE 2026 · Region 4 · Set 2 · Q28
(a) The two Kirchhoff's rules are based on law of conservation of two physical quantities. Name the quantities. (b) Find magnitude and direction of…
(a)
The two Kirchhoff's rules are based on law of conservation of two physical quantities. Name the quantities.
(b)
Find magnitude and direction of current in $\displaystyle 1 \Omega$ resistor in the given circuit.
Marking-scheme solution
(a)
Junction rule — it is based on the law of conservation of charge.
Loop rule — it is based on the law of conservation of energy.
(b)
Loop equation ($\displaystyle 1$): $\displaystyle 2 I_{1}+I_{2}+3 I_{1}=9$, so $\displaystyle 5 I_{1}+I_{2}=9 \quad \ldots(1)$
Loop equation ($\displaystyle 2$): $\displaystyle 3\left(I_{1}-I_{2}\right)-I_{2}=6$, $\displaystyle 3 I_{1}-3 I_{2}-I_{2}=6$, so $\displaystyle 3 I_{1}-4 I_{2}=6 \quad \ldots(2)$
Solving ($\displaystyle 1$) and ($\displaystyle 2$): $\displaystyle 4\left(5 I_{1}+I_{2}\right)=36$ and $\displaystyle 3 I_{1}-4 I_{2}=6$
On solving we get $\displaystyle 23 I_{1}=42 \Rightarrow I_{1}=\dfrac{42}{23} \mathrm{~A}$
Now solving for $\displaystyle I_{2}$: $\displaystyle I_{2}=9-5 I_{1}=-\dfrac{3}{23} \mathrm{~A}$
Direction of current in the $\displaystyle 1\ \Omega$ resistor is from Q to P.
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