Direct Current Circuit | Assignment Collection

Assignment 1

1. Define $1 \; \;  Ampere$ current. 

2. Describe the mechanism of metallic conduction. 

3. Show that one ampere is equivalent to a flow of $6.25 ∗ 10^{18}$ elementary charges per second. 

4. How many electrons pass through a lamp in one minute, if the current is $300\;  mA$? 

5. How many electrons per second flow through a filament of a $120 \; V$ and $60 \; W$ electric bulb? Given electric power is the product of voltage and current. 

6. The amount of charge passing through cross-section of a wire is $q(t) = at^2 + bt + c $

•     Write the dimensional formulae for a, b, c.
•     If the values of a, b and c in SI units are 5, 3, 1 respectively, find the value of current at $t = 5$ second.

Assignment 2

1. Define drift velocity and current density. Establish a relation between drift velocity of electrons and current density in the conductor. 

2. Define Ohm’s Law and discuss the experimental verification of Ohm’s law. (Only for section A) 

3. A copper wire has a diameter of $1.02 \; mm$ and carries a constant current of $1.67 \; A$. If the density of free electrons in copper is $8.5 ∗ 10^{28}/m^3$, calculate the current density and the drift velocity of the electrons. [Ans: $J = 2.04 ∗ 10^6 \; A/m^2$; $V_d = 1.5 ∗ 10^{-4}\; m/s$] 

4. A copper wire has a resistance of $10 \; \Omega$ and an area cross-section $1 \; mm^{2}$. A potential difference of $10 \; V$ exists across the wire. Calculate the drift speed of electrons if the number of electro per cubic meter in copper is $ 8 ∗ 10^{28}$ electrons. [Ans: $0.078 \;  mm/s $]

Assignment 3

1. Resistance of a wire of length $1\;m$, diameter $1\;mm$ is $2.2\; \Omega$. Calculate its resistivity and conductivity. [Ans: $\rho = 1.727 \; * \; 10^{-6}\; \Omega \;m$;   $5.79 * 10^ {-5} \; \Omega^{-1}\; m^{-1}$]

2. Two wires, one of copper and another of iron, have the same diameter and carry the same current. In which wire the drift velocity of electrons will be more?

3. A wire is stretched to double its length. What happens to its resistance and resistivity?

4. A wire having a diameter of $1.2 \; mm$ and resistivity of $100 * 10^{-8} \Omega \; m$ at $0^{0}C$ is connected across a cell of emf $1.5\;V$ and gives a current of $10\;mA$. Calculate the length of the wire. [Ans: $  169.6\;m $]

Assignment 4

1. Determine the voltage drop across the resistor $R_1$ in the circuit given below with $V = 60\;V$, $R_1 = 18\;Ohm$, $R_2 = 10\;Ohm$ [Answer = $45\; V$]

2. Two resistors of resistance $1000\; \Omega$ and $2000 \; \Omega$ are joined in series with a $100\; V$ supply. A voltmeter of internal resistance $4000 \; \Omega$ is connected to measure the potential difference across $1000 \; \Omega$ resistor. Calculate the reading shown by the voltmeter. [Answer: $28.57\; Volt$]

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