Home
Class 12
PHYSICS
The current through a wire varies with t...

The current through a wire varies with time as `I = I_(0) + alpha t `, where `I_(0) = 10` A and `alpha = 4 As^(-1)` . The charge that flows across a cross-section of the wire in first 10 seconds is .....

Text Solution

Verified by Experts

Current , I = `(dq)/(dt) = I_(0) + alpha t `
`therefore dq = (I_(0) + alpha t ) dt `
Integrating on both sides,
` Q = int dq = int_(t = 0)^(t = 10 ) (I_(0) + alpha t) dt `
`= int_(0)^(10) l_(0)" dt " + int_(0)^(10) alpha` t dt
`= I_(0) int_(0)^(10) dt + alpha int_(0)^(10) ` t dt
= `I_(0) [ t]_(0)^(10) + alpha [ (t^(2))/(2) ]_(0)^(10)`
` = 10I_(0) + 50 alpha `
Substituting ` I_(0) = 10 and alpha = 4 `
Q = 10 (10 ) + 50(4) = 300 C
Promotional Banner

Topper's Solved these Questions

  • CURRENT ELECTRICITY

    KUMAR PRAKASHAN|Exercise SECTION [B] (NUMERICAL)|10 Videos

  • CURRENT ELECTRICITY

    KUMAR PRAKASHAN|Exercise SECTION C NCERT EXEMPLAR SOLUTION (MULTIPLE CHOICE QUESTIONS (MCQs))|6 Videos

  • CURRENT ELECTRICITY

    KUMAR PRAKASHAN|Exercise SECTION [B] (NUMERICAL FROM TEXTUAL EXERCISE)|35 Videos

  • BOARD'S QUESTION PAPER MARCH-2020

    KUMAR PRAKASHAN|Exercise PART-B SECTION -C|4 Videos

  • DUAL NATURE OF RADIATION AND MATTER

    KUMAR PRAKASHAN|Exercise Section-D (MCQs asked in GUJCET/Board Exam)|1 Videos

Similar Questions

Explore conceptually related problems

The current through a wire varies with time as I= I_(0) + alpha t , where I_(0) = 1 A and alpha =4 As^(-1) . The charge that flows across a cross-section or the wire In first 10 seconds is ....

The current through a wire varies wilh time as I = I_(0) + alpha t where I_(0) = 20 A and alpha = 3 A s^(-1) . Find the charge that flows across a cross - section of the wire in first 10 seconds.

The current in conductor varies with time t as I = 2 t + 3 t^(2) where I is in ampere and t in seconds. Electric charge flowing through a section of the conductor during t = 2 sec to t = 3 sec is

The mutual inductance of the system of two coils is 5 mH. The current in the first coil varies according to the equation I = I_0 sinomegat , where I_0 = 10 A and omega = 100pi "rad s"^(-1) . The value of maximum induced emf in the second coil is ____

The current through a wire depends on time as i=(2+3t)A . Calculate the charge crossed through a cross section of the wire in 10sec.

The coefficient of linear expansion 'alpha ' of a rod of length 2 m varies with the distance x from the end of the rod as alpha = alpha_(0) + alpha_(1) "x" where alpha_(0) = 1.76 xx 10^(-5) "^(@)C^(-1)"and" alpha_(1) = 1.2 xx 10^(-6)m^(-1) "^(@)C^(-1) . The increase in the length of the rod. When heated through 100^(@)C is :-

The time dependence of a physical quantity P is given by P=P_(0) exp (-alpha t^(2)) , where alpha is a constant and t is time. The constant alpha

Two coils have a mutual inductance of 0.005H. The current changes in the first coil according to equation I=I_0 sin omegat , where I_0 = 10A and omega = 100pi rad/sec. The maximum value of emf in the second coil is ___

In a p-n junction diode, the current I can be expressed as I= I_(0) "exp" ((eV)/(2k_(B)T)-1) where I_(0) is called the reverse saturation current, V is the voltage across the diode and is positive for forward bias and negative for reverse bias, and I is the current through the diode, k_(B) is the Boltzmann constant (8.6 xx 10^(–5) eV//K) and T is the absolute temperature. If for a given diode I_(0) = 5 xx 10^(-12) A and T = 300 K, then (a) What will be the forward current at a forward voltage of 0.6 V? (b) What will be the increase in the current if the voltage across the diode is increased to 0.7 V? (c) What is the dynamic resistance? (d) What will be the current if reverse bias voltage changes from 1 V to 2 V?

A long straight cable of length l is placed symmetrically along z - axis and has radius a(lt lt l) . The cable consists of a thin wire and a co-axial conducting tube. An alternating current thin wire and returns along the coaxial conducting tube. The induced electric field at a distance s from the wire inside the cable is vec(E )(s, t)=mu_(0)I_(0)v cos (2pi vt) ln ((s)/(a))hat(k) Integrate the displacement current density across the cross - section of the cable to find the total displacement current I^(d) .