Question

A coil of n turns and resistance R Ω is connected in series with a resistance `"R"/2`. The combination is moved for time t second through magnetic flux ϕ₁ to ϕ₂, The induced current in the circuit is ______.

Options

• `("n"(phi_1-phi_2))/(3"Rt")`

• `(2"n"(phi_1-phi_2))/(3"Rt")`

• `(2"n"(phi_1-phi_2))/("Rt")`

• `("n"(phi_1-phi_2))/("Rt")`

Answer 1

A coil of n turns and resistance R Ω is connected in series with a resistance `"R"/2`. The combination is moved for time t second through magnetic flux ϕ₁ to ϕ₂, The induced current in the circuit is `(2"n"(phi_1-phi_2))/(3"Rt")`.

Explanation:

When a coil of n turns moves through a magnetic flux from ϕ₁ to ϕ₂, the emf induced in the coil is

`epsilon = -("nd"phi)/"dt"=(-n(phi_2-phi_1))/1=(n(phi_1-phi_2))/"t"`    ...(i)

As, resistance R of coil and `"R"/2` are in series, so equivalent resistance is

`"R"_"eq"="R"+"R"/2=(3"R")/2`   ...(ii)

The induced current in the circuit is,

`"I"="e"/("R"_"eq")=(n(phi_2-phi_1))/("t"((3"R")/2))=(2"n"(phi_1-phi_2))/(3"Rt")`