For a certain device, the current \(I\) changes with the voltage \(V\) as \(I=kV^{2}\), where \(k\) is a constant. The resistance \(R=V/I\) of the device is 50 Ω at 2 V. Its resistance at 4 V is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25 Ω
The relation \( V=IR \) defines the resistance of any device. The device obeys Ohm’s law only if this \( R \) stays the same at all voltages. Here \( I \) is not proportional to \( V \), so \( R \) changes with \( V \).
\( \begin{aligned} R &= \frac{V}{I} \\ &= \frac{V}{kV^{2}} \\ &= \frac{1}{kV} \end{aligned} \)
So \( R \) is inversely proportional to \( V \).
\( \begin{aligned} R_2 &= R_1\times\frac{V_1}{V_2} \\ &= 50\times\frac{2}{4} \\ &= 25\ \Omega \end{aligned} \)
NCERT (2026-27):
Points to Ponder – “… The assertion that V = IR is a statement of Ohm’s law is not true. This equation defines resistance and it may be applied to all conducting devices whether they obey Ohm’s law or not. The Ohm’s law asserts that the plot of I versus V is linear i.e., R is independent of V.”