Learn current definition in physics and relation between drift velocity and current. Practice direction of current in the given conductor through an area and instantaneous and average current.

Current is defined as the motion of charges.

- Consider an isolated metallic conductor in which electrons are moving randomly.
- The rate of flow of electrons from left to right at any point P is same as the rate of flow of electrons from right to left due to random motion of electrons.
- So, net rate of flow of current is zero.

- The direction of current is in the direction of flow of positive charge and opposite to the direction of flow of negative charge.

A Right to left

B Left to right

C Upward

D downward

- Consider a metallic wire of area A through which charged particles are flowing.

- Let \(\Delta Q\) be the amount of charge passing through area A in \(\Delta t\) time interval.
- The average current through this area is the rate of flow of charges passing through it.

\(I_{avg}=\dfrac {\Delta Q}{\Delta t}\)

and instantaneous current

\(I= \displaystyle\lim_{\Delta t \to 0} \dfrac {\Delta Q}{\Delta t}=\dfrac {dQ}{dt} \)

- Drift velocity of charges can be understood from the concept of river-boat.
- Consider a situation of river boat in which boat has to reach from point P to A. But due to flow of river, the boat reaches at some point B.
- The distance between point A and B is known as drift.

- Similarly in conductors in the absence of an electric field, electrons move randomly.
- When electric field is applied, electrons drift in some direction due to force on electrons. This direction is in the direction of force means opposite to the direction of electric field.

A In the same direction of electric field

B In the opposite direction of electric field

C Perpendicular direction to electric field

D None of these

- Consider a conductor of cross - sectional area A. Let "e" be the charge on each electron and "n" is the number of free electron per unit volume.

- Volume of conductor = \(A\,v_d\;\Delta t\)
- Charge crossing this area in \(\Delta t\) time

\(\Delta Q=n\,A\,v_d\,\Delta t\,e\)

\(i=\dfrac {\Delta Q}{\Delta t}\)

\(i = n\,A\,v_d\,e\)

A n gets halved

B \(v_d\) gets tripled

C Current gets halved

D current gets doubled

- Consider a current flowing through a conductor as a function of time \(I\) = f (t)

We know,

\(I=\dfrac {dQ}{dt}\)

\(f(t)=\dfrac {dQ}{dt}\)

or, \(dQ=f(t)\, dt\)

or, \(\int\limits_0^QdQ=\int\limits_0^t\,f(t) \,dt\)

\(Q(t)=\int\limits_0^t f(t)\,dt\)

Differentiation of Exponential / Logarithmic Function

**\(\dfrac {d}{dt}e^t=e^t; \ \\\dfrac {d}{dt}ln\ t=\dfrac {1}{t}\)**

- Consider, a charge 'q' rotating in a circle attached at the end of an insulating string of length 'r' with constant angular velocity \(\omega\). It is equivalent to current carrying loop.

\(I_{eq}=\dfrac {q}{T}\)

- Time period of revolution, \(T=\dfrac {2\pi}{\omega}\)

\(I_{avg}=\dfrac {q}{\dfrac {2\pi}{\omega}}\)

\(I_{avg}=\dfrac {\omega\,q}{2\pi}{}\)

A \(\dfrac {\omega}{\pi}(q_1+q_2)\)

B \(\omega(q_1+q_2)\)

C \(\dfrac {\omega}{2\pi}(q_1+q_2)\)

D \(\dfrac {\omega}{\pi}(q_1-q_2)\)

The relation between drift velocity and current is given by** **

**\(i =nAv_de\)**

A 50 \(\mu\) m/sec

B 60 \(\mu\) m/sec

C 39 \(\mu\)m/sec

D 36 \(\mu\) m/sec