If the magnetic flux through a coil at any time t is given by φ=(4t2+5t-3) , then the increase in induced emf (in volt) 2 second after t = 0 is

Question

If the magnetic flux through a coil at any time t is given by φ=(4t2+5t-3) , then the increase in induced emf (in volt) 2 second after t = 0 is (A)  5  (B)  16  (C)  21  (D) zero

Tardigrade Admin · Accepted Answer

As φ=4t2+5t-3 ∴ The induced emf in the coil is ε=(d φ/dt) (in magnitude) =(d/dt)(4t2+5t+3)=8t+5V At t=0, ε1=5V and at t=2 s, ε2=21 V ∴ The increase in induced emf is Δε=ε2-ε1=21 V-5V =16 V

Q. If the magnetic flux through a coil at any time $t$ is given by $ϕ = (4 t^{2} + 5 t - 3)$ , then the increase in induced emf (in volt) $2$ second after $t = 0$ is

$5$

$16$

$21$

zero

As $ϕ = 4 t^{2} + 5 t - 3$
$∴$ The induced emf in the coil is
$ε = \frac{d ϕ}{d t}$ (in magnitude)
$= \frac{d}{d t} (4 t^{2} + 5 t + 3) = 8 t + 5 V$
At $t = 0, ε_{1} = 5 V$ and at $t = 2 s, ε_{2} = 21 V$
$∴$ The increase in induced emf is
$Δ ε = ε_{2} - ε_{1} = 21 V - 5 V$
$= 16 V$

Q. If the magnetic flux through a coil at any time t is given by ϕ=(4t2+5t−3) , then the increase in induced emf (in volt) 2 second after t=0 is

5

16

21

zero

As ϕ=4t2+5t−3 ∴ The induced emf in the coil is ε=dtdϕ​ (in magnitude) =dtd​(4t2+5t+3)=8t+5V At t=0,ε1​=5V and at t=2s,ε2​=21V ∴ The increase in induced emf is Δε=ε2​−ε1​=21V−5V =16V

Q. If the magnetic flux through a coil at any time $t$ is given by $ϕ = (4 t^{2} + 5 t - 3)$ , then the increase in induced emf (in volt) $2$ second after $t = 0$ is

$5$

$16$

$21$

As $ϕ = 4 t^{2} + 5 t - 3$
$∴$ The induced emf in the coil is
$ε = \frac{d ϕ}{d t}$ (in magnitude)
$= \frac{d}{d t} (4 t^{2} + 5 t + 3) = 8 t + 5 V$
At $t = 0, ε_{1} = 5 V$ and at $t = 2 s, ε_{2} = 21 V$
$∴$ The increase in induced emf is
$Δ ε = ε_{2} - ε_{1} = 21 V - 5 V$
$= 16 V$