Question
Question: The current through a wire depends on time as \(i = {i_0} + \alpha t\) where \({i_0} = 10A\) and \(\...
The current through a wire depends on time as i=i0+αt where i0=10A and α=4As−1. Find the charge crossed through a section of the wire in 10 seconds.
Solution
The charge is the property of particles that attract and repulse with each other when placed in an electrical field. The rate of flow of charges is called current. Applying the formula for charge integrates the equation using the given data to obtain the charge crossed through a section in the given time period.
Formula used:
q=∫idt
Here q is the charge, i is current, t is the time.
Complete step by step answer:
The charge is the property of particles that attract and repulse with each other when placed in an electrical field. A charged particle exert force on each other. The square of the distance between two particles is inversely proportional to the force due to the charge. The SI unit of charge is the coulomb.
1.6×1019 is the charge of a single electron. The electronic circuit uses an electric charge to do some useful work. The moving charges produce an electric current. The rate of flow of charges is called current. The SI unit of current is ampere. One ampere equals one coulomb per second. The current is measured in the circuit using an ammeter.
Charge crossed through a section of the wire
q=∫idt
Now integrate the above equation
q=0∫tidt
Substitute the value of iin the above equation
q=0∫t(i0+αt)dt
q=i0t+α2t2
Now substitute the values to obtain the charge
q=10×10+4×210×10
q=300C(Answer).
Note: Fundamental property that attracts or repulses each other when placed in the magnetic field is called charge. When the linear size of a charged body is smaller than the distance, then the size can be ignored and that charge body is called point charge. The process of giving charge to a body is called electrification. The charge experiences field is only in the electric field.