GATE 2026 EE Q.23: solution and answer

Official answer: BSource: Official answer key, GATE 2026 EE (IIT Guwahati)

1. What a linear element is. A two-terminal element is linear when its $v$–$i$ relation obeys superposition (additivity and homogeneity). If excitations $x_1$ and $x_2$ give responses $y_1$ and $y_2$, then the excitation $a{x}_1+b{x}_2$ must give $a{y}_1+b{y}_2$ for every pair of real constants $a$ and $b$, negative ones included.

2. Resistor. Ohm's law, $v=Ri$ with $R$ constant, is a straight line through the origin of the $v$–$i$ plane. So $R(a{i}_1+b{i}_2)=a{v}_1+b{v}_2$, and R is linear.

3. Inductor. $v=L\frac{di}{dt}$ with $L$ constant. Differentiation is a linear operation: $L\frac{d}{dt}(a{i}_1+b{i}_2)=aL\frac{d{i}_1}{dt}+bL\frac{d{i}_2}{dt}=a{v}_1+b{v}_2$. So L is linear.

4. Capacitor. $i=C\frac{dv}{dt}$ with $C$ constant. The same argument applies: $C\frac{d}{dt}(a{v}_1+b{v}_2)=a{i}_1+b{i}_2$. So C is linear.

5. Ideal diode. It conducts with $v=0$ for $i\ge 0$ and blocks with $i=0$ for $v\le 0$. Its $v$–$i$ characteristic is two half-lines that meet at a corner at the origin, not a single straight line through the origin. To show homogeneity fails, take the allowed operating point $(v,i)=(0,1\text{A})$ and scale it by $k=-1$. That gives $(0,-1\text{A})$, and an ideal diode cannot carry reverse current, so that point is not on its characteristic. D is therefore nonlinear. It is piecewise linear, but piecewise linear is not linear. The Shockley model $i=I_S\left(e^{v/\eta V_T}-1\right)$ is nonlinear too.

6. Conclusion. The linear elements in the circuit are R, L and C. The diode is the only nonlinear element. The answer is option (B).