Home
Class 12
PHYSICS
Two different coils have self-inductance...

Two different coils have self-inductance `L_(1)=8mH,L_(2)=2mH`. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are `i_(1),V_(1)andW_(1)` respectively. Corrseponding values for the second coil at the same instant are `i_(2),V_(2)andW_(2)` respectively. Then,

A

`(i_(1))/(i_(2)) = (1)/(4)`

B

`(i_(1))/(i_(2)) = 4`

C

`(W_(1))/(W_(2)) = (1)/(4)`

D

`(V_(1))/(V_(2)) = 4`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`V_(1) = L_(1) (dI_(1))/(dt)` and `V_(2) = L_(2) (dI_(2))/(dt)`
But `(dI_(1))/(dt) = (dI_(2))/(dt)` (given) `:. (V_(1))/(V_(2)) = (L_(1))/(L_(2)) = (8)/(2) = (4)/(1)`
Again, same power is given to the two coils.
`:. V_(1)I_(1) = V_(2)I_(2)` or `(I_(1))/(I_(2)) = (V_(2))/(V_(1)) = (1)/(4)`
Again, energy `= (1)/(2) LI^(2)`
`:. (W_(2))/(W_(1)) = ((1)/(2) L_(2)I_(2)^(2))/((1)/(2) L_(1)I_(1)^(2)) = ((L_(2))/(L_(1)))((L_(2))/(I_(1)))^(2) = (2)/(8) (4)^(2) = (4)/(1)`
Promotional Banner

Topper's Solved these Questions

  • INDUCTANCE

    CENGAGE PHYSICS ENGLISH|Exercise Archives (linked Compreshension)|8 Videos

  • INDUCTANCE

    CENGAGE PHYSICS ENGLISH|Exercise Archives (integer)|2 Videos

  • INDUCTANCE

    CENGAGE PHYSICS ENGLISH|Exercise Archives (single Correct )|8 Videos

  • HEATING EFFECT OF CURRENT

    CENGAGE PHYSICS ENGLISH|Exercise Thermal Power in Resistance Connected in Circuit|27 Videos

  • MAGNETIC FIELD AND MAGNETIC FORCES

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct Answer type|2 Videos

Similar Questions

Explore conceptually related problems

Two different coils have self-inductances L_(1) = 8 mH and L_(2) = 2 mH . The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coil is the same. At that time, the current, the induced voltage and the energy stored in the first coil are i_(1), V_(1) and W_(1) respectively. Corresponding values for the second coil at the same instant are i_(2), V_(2) and W_(2) respectively. Then:

Two different coils have self inductances L_1=9mH and L_2=2mH . The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coils is the same. At that time, the current the induced voltage and the energy stored in the first coil are i_1,V_1 and W_1 respectively. Corresponding values for the second coil at the same instant are i_2,V-2 and W_2 respectively. Then,

Two different coils have self inductances L_(1)=8mH and L_(2)=2mH . The current in both the coil is increased at same constant rate. At a certain instant power given to two coils is same. At that time the energy stored in both the coils are V_(1) & V_(2) respectively, then (V_(1))/(V_(2)) is

Two different coils have self- inductances L_(1) = 16 mH and L_(2)= 12 mH. At a certain instant, the current in the two coils is increasing at the same rate and power supplied to the two coils is the same. Find the ratio of i) induced voltage ii) current iii) energy stored in the two coils at that instant.

Two coils having self-inductances, L_(1)=5mH and L_(2)=1mH . The current in the coil is increasing of same constant rate at a certain instant and the power supplied to the coils is also same, Find the ratio of (i) induced voltage (ii) current (iii) energy stored in two coils at that instant

Two coils have self-inductance L_(1) = 4mH and L_(2) = 1 mH respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both coils are given the same power. If I_(1) and I_(2) are the currents in the two coils, at that instant of time respectively, then the value of (I_(1)//I_(2)) is :

Two coils have self inductances L_(1)=4 mH and L_(2)=8mH . Current in both the coils is increasing at same rate. At an instant, when the power given to the two coils is same, find (i) Ratio of current in the inductors. (ii) Ratio of potential difference (iii) Ratio of energy stored

In a coil of self-inductance 10mH, the current I (in ampere) varies with time t (in second) as i=8t+2amp

In a coil of self-inductance 10mH, the current I (in ampere) varies with time t (in second) as i=8t+2amp

A 50 mH coil carries a current of 2 ampere. The energy stored in joules is

Knowledge Check

  • Two different coils have self-inductances L_(1) = 8 mH and L_(2) = 2 mH . The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coil is the same. At that time, the current, the induced voltage and the energy stored in the first coil are i_(1), V_(1) and W_(1) respectively. Corresponding values for the second coil at the same instant are i_(2), V_(2) and W_(2) respectively. Then:

    A
    `(W_(2))/(W_(1))=8`
    B
    `(W_(2))/(W_(1))=(1)/(8)`
    C
    `(W_(2))/(W_(1))=4`
    D
    `(W_(2))/(W_(1))=(1)/(4)`

  • Two coils have self-inductance L_(1) = 4mH and L_(2) = 1 mH respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both coils are given the same power. If I_(1) and I_(2) are the currents in the two coils, at that instant of time respectively, then the value of (I_(1)//I_(2)) is :

    A
    `(1)/(8)`
    B
    `(1)/(4)`
    C
    `(1)/(2)`
    D
    1