# The current i flowing in a coil varies with time as shown in the figure. The variation of induced emf with time would be-

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The current i flowing in a coil varies with time as shown in the figure. The variation of induced emf with time would be-

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Induced emf,e = -L$\frac{di}{dt}$

For 0 ≤ t ≤  $\frac{T}{4}$,

i-t graph is a straight line with positive constant slop.

∴ $\frac{di}{dt}$ = constant

e = -ve and constant, For 0 ≤ t ≤ $\frac{T}{4}$

For $\frac{T}{4}$ ≤ t ≤ $\frac{T}{2}$

i is constant ∴ $\frac{di}{dt}$ = 0

e = 0$\frac{T}{4}$ ≤ t ≤ $\frac{T}{2}$

For $\frac{T}{2}$≤ t ≤ $\frac{3T}{4}$

i-t graph is a straight line with negative constant slope.

∴  $\frac{di}{dt}$ = constant

e = +ve and constant For $\frac{T}{2}$≤ t ≤ $\frac{3T}{4}$

For$\frac{3T}{4}$≤ t ≤ T,

i is zero ∴ $\frac{di}{dt}$ = 0

e = 0 For $\frac{3T}{4}$≤ t ≤ T

From this analysis, the variation of induced emf with time as shown in the figure below.