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Science · 2024 · 5 marks
CBSE 2024 · Region 5 · Set 1 · Q36
(i)The potential difference across the two ends of a circuit component is decreased to one-third of its initial value, while its resistance remains constant. What change will be observed in the current flowing through it ? Name and state the law which helps us to answer this question.(ii)Draw a schematic diagram of a circuit consisting of a battery of four $\displaystyle 1 \cdot 5 \mathrm{~V}$ cells, a $\displaystyle 5 \Omega$ resistor, a $\displaystyle 10 \Omega$ resistor and a $\displaystyle 15 \Omega$ resistor and a plug key, all connected in series. Now find(I)the electric current passing through the circuit, and(II)potential difference across the $\displaystyle 10 \Omega$ resistor when the plug key is closed.(i)When is the potential difference between two points said to be $\displaystyle 1$ volt?(ii)A copper wire has a diameter of $\displaystyle 0 \cdot 2 \mathrm{~mm}$ and resistivity of $\displaystyle 1 \cdot 6 \times 10^{-8} \Omega \mathrm{~m}$. What will be the length of this wire to make its resistance $\displaystyle 14 \Omega$ ? How much does the resistance change, if the diameter of the wire is doubled ?
(i)
The potential difference across the two ends of a circuit component is decreased to one-third of its initial value, while its resistance remains constant. What change will be observed in the current flowing through it ? Name and state the law which helps us to answer this question.
(ii)
Draw a schematic diagram of a circuit consisting of a battery of four $\displaystyle 1 \cdot 5 \mathrm{~V}$ cells, a $\displaystyle 5 \Omega$ resistor, a $\displaystyle 10 \Omega$ resistor and a $\displaystyle 15 \Omega$ resistor and a plug key, all connected in series. Now find
(I)
the electric current passing through the circuit, and
(II)
potential difference across the $\displaystyle 10 \Omega$ resistor when the plug key is closed.
(i)
When is the potential difference between two points said to be $\displaystyle 1$ volt?
(ii)
A copper wire has a diameter of $\displaystyle 0 \cdot 2 \mathrm{~mm}$ and resistivity of $\displaystyle 1 \cdot 6 \times 10^{-8} \Omega \mathrm{~m}$. What will be the length of this wire to make its resistance $\displaystyle 14 \Omega$ ? How much does the resistance change, if the diameter of the wire is doubled ?
Marking-scheme solution
(a)
(i) • Current becomes one-third of its initial value.
Ohm's Law
The potential difference across the ends of a conductor is directly proportional to the current flowing through it, provided its temperature remains the same.
Total Voltage \(\displaystyle =\mathrm{V}=4 \times 1 \cdot 5 \mathrm{~V}=6 \mathrm{~V}\) Total resistance, \(\displaystyle \mathrm{R}(\mathrm{s})=\mathrm{R}_{1}+\mathrm{R}_{2}+\mathrm{R}_{3}\)
\[=5 \Omega+10 \Omega+15 \Omega=30 \Omega
\]
(I)
Current, \(\displaystyle \mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{6 \mathrm{~V}}{30 \Omega}=0.2 \mathrm{~A}\)
(II)
\(\displaystyle \mathrm{V}=\mathrm{IR}=0.2 \mathrm{~A} \times 10 \Omega=2 \mathrm{~V}\)
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CBSE Class 10 Science past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.