The induced electromotive force (emf) $\varepsilon$ in a coil is proportional to the negative rate of change of current with respect to time. The relationship is given by the formula: $\varepsilon = -L \frac{di}{dt}$ Where $L$ is the self-inductance of the coil .

Analysis of the Relationship:

1. Dependence on Slope: The induced emf is determined by the slope of the current vs. time graph ($di/dt$). The negative sign indicates that the emf opposes the change in current (Lenz's Law).
2. Constant Slope: If the current changes linearly (constant slope), $\frac{di}{dt}$ is constant, resulting in a constant induced emf.

• Positive Slope: If $i$ increases linearly, $\frac{di}{dt} > 0$, so $\varepsilon$ is negative and constant.
• Negative Slope: If $i$ decreases linearly, $\frac{di}{dt} < 0$, so $\varepsilon$ is positive and constant.
• Zero Slope: If $i$ is constant, $\frac{di}{dt} = 0$, so $\varepsilon = 0$.

Conclusion: The correct graph for induced emf vs. time will show constant negative values corresponding to rising current intervals, constant positive values corresponding to falling current intervals, and zero values where the current is constant.