✓ Board-verified
Science · 2026 · 5 marks
CBSE 2026 · Region 4 · Set 3 · Q39
(i)Derive an expression for the equivalent resistance of three resistors connected in parallel with a battery as shown in figure.
(ii)Find the values of the electric currents flowing through the resistors $\displaystyle \mathrm{R}_{1}, \mathrm{R}_{2}$ and $\displaystyle \mathrm{R}_{3}$ in the given electric circuit.(i)Define electrical resistivity of a material.(ii)How will the resistivity and resistance of a conducting wire change if the length and area of cross-section of wire both are doubled ? Justify your answer.(iii)Calculate the electric current flowing through a $\displaystyle 4 \Omega$ resistor that produces $\displaystyle 100$ J of heat every second. { } $\displaystyle 1190$-$\displaystyle 3$
(i)
Derive an expression for the equivalent resistance of three resistors connected in parallel with a battery as shown in figure.
(ii)
Find the values of the electric currents flowing through the resistors $\displaystyle \mathrm{R}_{1}, \mathrm{R}_{2}$ and $\displaystyle \mathrm{R}_{3}$ in the given electric circuit.
(i)
Define electrical resistivity of a material.
(ii)
How will the resistivity and resistance of a conducting wire change if the length and area of cross-section of wire both are doubled ? Justify your answer.
(iii)
Calculate the electric current flowing through a $\displaystyle 4 \Omega$ resistor that produces $\displaystyle 100$ J of heat every second. { } $\displaystyle 1190$-$\displaystyle 3$
Marking-scheme solution
(i)
As in parallel combination, potential difference applied across each resistor is same. Current flowing through each resistor \(\displaystyle \mathrm{R}_{1}, \mathrm{R}_{2}\) and \(\displaystyle \mathrm{R}_{3}\) is
\[I_{1}=\frac{V}{R_{1}}, I_{2}=\frac{V}{R_{2}}, I_{3}=\frac{V}{R_{3}}
\]
Current, \(\displaystyle \mathrm{I}=\mathrm{I}_{1}+\mathrm{I}_{2}+\mathrm{I}_{3}\)
\[\begin{aligned}
& \frac{\mathrm{V}}{\mathrm{R}_{\mathrm{p}}}=\frac{\mathrm{V}}{\mathrm{R}_{1}}+\frac{\mathrm{V}}{\mathrm{R}_{2}}+\frac{\mathrm{V}}{\mathrm{R}_{3}} \\
& \frac{1}{\mathrm{R}_{\mathrm{p}}}=\frac{1}{\mathrm{R}_{1}}+\frac{1}{\mathrm{R}_{2}}+\frac{1}{\mathrm{R}_{3}}
\end{aligned}
\]
(ii)
As all the resistors are connected in parallel, the potential difference applied across each resistor is $\displaystyle 12$ V
\(\displaystyle \mathrm{V}=\mathrm{IR}\)
\(\displaystyle \mathrm{I}_{1}=\frac{\mathrm{V}}{\mathrm{R}_{1}}=\frac{12}{2}=6 \mathrm{~A}\)
\(\displaystyle \mathrm{I}_{2}=\frac{12}{4}=3 \mathrm{~A}\)
\(\displaystyle \mathrm{I}_{3}=\frac{12}{6}=2 \mathrm{~A}\)
(i)
Resistivity is the resistance offered by a wire of unit length and unit area of cross section in an electric circuit.
(ii)
Resistivity of conducting wire will remain same.
Resistivity is the characteristic property of the material.
Resistance will remain same
More from Electricity
- In domestic electric circuits the wiring with 15 A current rating is for the electric devices which have2023 · asked 3×
- Assertion: Electrons move from lower potential to higher potential in a conductor. Reason (R): A dry cell…2024 · asked 3×
- The resistance of a wire of 0.01 cm radius and 1.0 cm length is 7 Ω. Calculate its resistivity. OR An…2026 · asked 3×
- Four identical resistors of 12 Ω each are connected in series to form a square ABCD as shown in the figure.…2025 · asked 3×
- The resistance of a wire of 0.01 cm radius is 7 ohms. If the resistivity of the material of the wire is 44 ×…2025 · asked 3×
- Read the following passage and answer the questions that follow: Swati, a class 10 student, observes that…2026 · asked 3×
- For verifying Ohm's law, we design an electric circuit diagram in which we show the arrangement of different…2023 · asked 3×
- The minimum number of identical bulbs of rating 4V; 6W, that can work safely with desired brightness, when…2025 · asked 3×
CBSE Class 10 Science past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.