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7.The self-induced emf in a 0.2 H coil when a current in it is changing at the rate of 100 A /sec is​

Answer 1

Answer:

$\boxed{\mathfrak{Self-induced \ EMF \ (\epsilon) = 20 \ V}}$

Given:

Self inductance (L) = 0.2 H

Rate of change of current ($\sf \dfrac{di}{dt}$) = 100 A/s

Explanation:

Self-induced EMF in coil when current varies through the coil:

$\boxed{ \bf{ \epsilon = L\dfrac{di}{dt}}}$

By substituting values in the equation we get:

$\rm \implies \epsilon = L\dfrac{di}{dt} \\ \\ \rm \implies \epsilon = 0.2 \times 100 \\ \\ \rm \implies \epsilon = 20 \: V$

Answer 2

GIVEN :-

• Sᴇʟғ ɪɴᴅᴜᴄᴛᴀɴᴄᴇ = $\bf\red{L}$ = 0.2L

• Rᴀᴛᴇ ᴏғ ᴄᴜʀʀᴇɴᴛ ғʟᴏᴡ = $\bf\red{\dfrac{dI}{dt}}$ = 100A/sᴇᴄ

TO FIND :-

• Iɴᴅᴜᴄᴇᴅ ᴇ.ᴍ.ғ .

SOLUTION :-

Wᴇ ʜᴀᴠᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

• $\bf\pink{N\:\phi\:=\:L\:I}$

Wʜᴇʀᴇ,

• N = ɴᴏ. ᴏғ ᴄᴏɪʟs .

• $\bf{\phi}$ = ᴍᴀɢɴᴇᴛɪᴄ ғʟᴜx .

• L = sᴇʟғ ɪɴᴅᴜᴄᴛᴀɴᴄᴇ .

• I = ᴄᴜʀʀᴇɴᴛ ғʟᴏᴡ .

Nᴏᴡ, ᴅɪғғᴇʀᴇɴᴛɪᴀᴛᴇ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇǫᴜᴀᴛɪᴏɴ,

$\bf{\implies\:\dfrac{d(N\phi)}{dt}\:=\:\dfrac{d(L\:I)}{dt}\:}$

$\rm{\implies\:N\dfrac{d\phi}{dt}\:=\:L\dfrac{d\:I}{dt}\:}$ ----(1)

Wᴇ ʜᴀᴠᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

$\huge\orange\star$ $\huge\bf{\gray{\underline{\pink{\boxed{\purple{\varepsilon\:=\:N\dfrac{d\phi}{dt}\:}}}}}}$

Wʜᴇʀᴇ,

• $\huge\bf\red{\varepsilon}$ = ᴇ.ᴍ.ғ ᴏғ ᴛʜᴇ ᴄᴏɪʟ .

Nᴏᴡ, ᴘᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴀʙᴏᴠᴇ ғᴏʀᴍᴜʟᴀ ɪɴ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ(1)

$\bf{\implies\:\varepsilon\:=\:L\dfrac{d\:I}{dt}\:}$

$\rm{\implies\:\varepsilon\:=\:0.2\times{100}}$

$\bf\green{\implies\:\varepsilon\:=\:20\:v}$

$\huge\red\therefore$ Tʜᴇ ᴇ.ᴍ.ғ ᴏғ ᴛʜᴇ ᴄᴏɪʟ ɪs "20ᴠ" .