✓ Board-verified
Science · 2025 · 2 marks
CBSE 2025 · Region 1 · Set 3 · Q22
(a) Consider two lamps A and B of rating 50 W; 220 V and 25 W; 220 V respectively. Find the ratio of the resistances of the two lamps (i.e. R_A: R_B…
(a)
Consider two lamps A and B of rating $\displaystyle 50$ W; $\displaystyle 220$ V and $\displaystyle 25 \mathrm{~W} ; 220 \mathrm{~V}$ respectively. Find the ratio of the resistances of the two lamps (i.e. $\displaystyle \mathrm{R}_{\mathrm{A}}: \mathrm{R}_{\mathrm{B}}$ ).
OR
(b)
Heat produced per second due to a current in a resistor of $\displaystyle 4 \Omega$ is $\displaystyle 400$ joules. Calculate the potential difference across the resistor.
Marking-scheme solution
\(\displaystyle \mathrm{P}=\frac{V^{2}}{R}\)
\[\begin{aligned}
\mathrm{R} & =\frac{V^{2}}{P} \\
R_{A} & =\frac{(220)^{2}}{50} \\
R_{B} & =\frac{(220)^{2}}{25} \\
\frac{R_{A}}{R_{B}} & =\frac{1}{2}
\end{aligned}
\]
/
\(\displaystyle \mathrm{P}=\frac{V^{2}}{R}\)
Since V is same means P is inversely proportional to R.
Power of lamp A is double that of B hence Resistance of A is half that of B.
\[\frac{R_{A}}{R_{B}}=\frac{1}{2}
\]
\[\begin{aligned}
& \mathrm{H}=\frac{V^{2}}{R} \times t \\
& 400=\frac{V^{2}}{4} \times 1 \\
& V^{2}=1600 \\
& \mathrm{~V}=40 \mathrm{~V}
\end{aligned}
\]
More from Electricity
- (i) Consider the following electric circuit: Calculate the values of the following: (I) Total resistance of the circuit. (II) The total electric…2026
- A 2000 W heater has a resistance of about 25 Ω, whereas a 100 W bulb has a resistance of 500 Ω. When 220 V is applied on these, then which of the two…2024
- Show how you would connect three resistors each of resistance 6 Ω, so that the combination has a resistance of 9 Ω. Also justify your answer. OR In…2024
- In domestic electric circuits the wiring with 15 A current rating is for the electric devices which have2023
- Assertion: Electrons move from lower potential to higher potential in a conductor. Reason (R): A dry cell maintains electric potential difference…2024
- (i) State whether the currents and potential difference in all the bulbs will be same or different when in a circuit three bulbs of: same wattage are…2024
- Study the given electric circuit in which 2 A electric current is flowing between points X and Y. (i) Using the battery, key, voltmeter and ammeter…2026
- Consider the following combinations of resistors: The combinations having equivalent resistance 1 Ω is/are:2024
CBSE Class 10 Science past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.