Electric current, drift velocity and mobility — practice questions

Question 1 · difficulty L2 · understanding

The current in a conductor is expressed as $I=3 t^2+4 t^3$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1 \mathrm{~s}$ to $t=2 \mathrm{~s}$ is __________ C.

Question 2 · difficulty L2 · understanding

The number density of free electrons in copper is nearly $$8 \times 10^{28} \mathrm{~m}^{-3}$$. A copper wire has its area of cross section $$=2 \times 10^{-6} \mathrm{~m}^{2}$$ and is carrying a current of $$3.2 \mathrm{~A}$$. The drift speed of the electrons is ___________ $$\times 10^{-6} \mathrm{ms}^{-1}$$

Question 3 · difficulty L2 · understanding

A current of $$2 \mathrm{~A}$$ flows through a wire of cross-sectional area $$25.0 \mathrm{~mm}^{2}$$. The number of free electrons in a cubic meter are $$2.0 \times 10^{28}$$. The drift velocity of the electrons is __________ $$\times 10^{-6} \mathrm{~ms}^{-1}$$ (given, charge on electron $$=1.6 \times 10^{-19} \mathrm{C}$$ ).

Question 4 · difficulty L2 · understanding

The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 $$\times$$ 10 6 A/m 2 . The current through the outer portion of the wire between radial distances $${r \over 2}$$ and r is x$$\pi$$ A; where x is __________.

Question 5 · difficulty L2 · understanding

The current density in a cylindrical wire of radius 4 mm is 4 $$\times$$ 10 6 Am $$-$$2 . The current through the outer portion of the wire between radial distances $${R \over 2}$$ and R is ____________ $$\pi$$ A.

Question 6 · difficulty L2 · understanding

A cylindrical wire of radius 0.5 mm and conductivity 5 $$\times$$ 10 7 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x 3 $$\pi$$ mA. The value of x is _________.

Question 7 · difficulty L2 · understanding

Which one of the following is not a measurable quantity?

• A. Resistance
• B. Voltage difference
• C. Displacement current
• D. Voltage

Question 8 · difficulty L2 · understanding

Current passing through a wire as function of time is given as $I(t)=0.02 t+0.01 \mathrm{~A}$. The charge that will flow through the wire from $t=1 \mathrm{~s}$ to $t=2 \mathrm{~s}$ is

• A. 0.02 C
• B. 0.07 C
• C. 0.06 C
• D. 0.04 C

Question 9 · difficulty L2 · understanding

The drift velocity of electrons for a conductor connected in an electrical circuit is $$\mathrm{V}_{\mathrm{d}}$$. The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

• A. $$\frac{V_{d}}{4}$$
• B. $$\mathrm{V}_{\mathrm{d}}$$
• C. $$2 \mathrm{~V}_{\mathrm{d}}$$
• D. $$\frac{V_{d}}{2}$$

Question 10 · difficulty L2 · understanding

Which of the following physical quantities have the same dimensions?

• A. Electric displacement $$(\overrightarrow{\mathrm{D}})$$ and surface charge density
• B. Displacement current and electric field
• C. Current density and surface charge density
• D. Electric potential and energy