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Physics · Textbook solutions

Current Electricity

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 16 questions

Worked Examples

7 q

Solved Examples

Worked · 7
  1. Eg 3.1
    (a) Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0×10−7 m21.0 \times 10^{-7}\,\text{m}^2 carrying a current of 1.5 A1.5\,\text{A}. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0×103 kg/m39.0 \times 10^{3}\,\text{kg/m}^{3}, and its atomic mass is 63.5 u63.5\,\text{u}. (b) Compare the drift speed obtained above with, (i) thermal speeds of copper atoms at ordinary temperatures, (ii) speed of propagation of electric field along the conductor which causes the drift motion.
  2. Eg 3.2
    (a) In Example 3.1, the electron drift speed is estimated to be only a few mm s−1\text{mm s}^{-1} for currents in the range of a few amperes? How then is current established almost the instant a circuit is closed? (b) The electron drift arises due to the force experienced by electrons in the electric field inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady average drift speed? (c) If the electron drift speed is so small, and the electron's charge is small, how can we still obtain large amounts of current in a conductor? (d) When electrons drift in a metal from lower to higher potential, does it mean that all the 'free' electrons of the metal are moving in the same direction? (e) Are the paths of electrons straight lines between successive collisions (with the positive ions of the metal) in the (i) absence of electric field, (ii) presence of electric field?
  3. Eg 3.3
    An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room temperature (27.0 ∘C27.0\,^\circ\text{C}) is found to be 75.3 Ω75.3\,\Omega. When the toaster is connected to a 230 V230\,\text{V} supply, the current settles, after a few seconds, to a steady value of 2.68 A2.68\,\text{A}. What is the steady temperature of the nichrome element? The temperature coefficient of resistance of nichrome averaged over the temperature range involved, is 1.70×10−4 ∘C−11.70 \times 10^{-4}\,^\circ\text{C}^{-1}.
  4. Eg 3.4
    The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω5\,\Omega and at steam point is 5.23 Ω5.23\,\Omega. When the thermometer is inserted in a hot bath, the resistance of the platinum wire is 5.795 Ω5.795\,\Omega. Calculate the temperature of the bath.
  5. Eg 3.5
    A battery of 10 V10\,\text{V} and negligible internal resistance is connected across the diagonally opposite corners of a cubical network consisting of 12 resistors each of resistance 1 Ω1\,\Omega (Fig. 3.16). Determine the equivalent resistance of the network and the current along each edge of the cube.
  6. Eg 3.6
    Determine the current in each branch of the network shown in Fig. 3.17.
  7. Eg 3.7
    The four arms of a Wheatstone bridge (Fig. 3.19) have the following resistances: AB =100 Ω= 100\,\Omega, BC =10 Ω= 10\,\Omega, CD =5 Ω= 5\,\Omega, and DA =60 Ω= 60\,\Omega. A galvanometer of 15 Ω15\,\Omega resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V10\,\text{V} is maintained across AC.

Exercises

9 q
  1. Ex 3.1
    The storage battery of a car has an emf of 12 V12\,\text{V}. If the internal resistance of the battery is 0.4 Ω0.4\,\Omega, what is the maximum current that can be drawn from the battery?
  2. Ex 3.2
    A battery of emf 10 V10\,\text{V} and internal resistance 3 Ω3\,\Omega is connected to a resistor. If the current in the circuit is 0.5 A0.5\,\text{A}, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?
  3. Ex 3.3
    At room temperature (27.0 ∘C27.0\,^\circ\text{C}) the resistance of a heating element is 100 Ω100\,\Omega. What is the temperature of the element if the resistance is found to be 117 Ω117\,\Omega, given that the temperature coefficient of the material of the resistor is 1.70×10−4 ∘C−11.70 \times 10^{-4}\,^\circ\text{C}^{-1}.
  4. Ex 3.4
    A negligibly small current is passed through a wire of length 15 m15\,\text{m} and uniform cross-section 6.0×10−7 m26.0 \times 10^{-7}\,\text{m}^2, and its resistance is measured to be 5.0 Ω5.0\,\Omega. What is the resistivity of the material at the temperature of the experiment?
  5. Ex 3.5
    A silver wire has a resistance of 2.1 Ω2.1\,\Omega at 27.5 ∘C27.5\,^\circ\text{C}, and a resistance of 2.7 Ω2.7\,\Omega at 100 ∘C100\,^\circ\text{C}. Determine the temperature coefficient of resistivity of silver.
  6. Ex 3.6
    A heating element using nichrome connected to a 230 V230\,\text{V} supply draws an initial current of 3.2 A3.2\,\text{A} which settles after a few seconds to a steady value of 2.8 A2.8\,\text{A}. What is the steady temperature of the heating element if the room temperature is 27.0 ∘C27.0\,^\circ\text{C}? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70×10−4 ∘C−11.70 \times 10^{-4}\,^\circ\text{C}^{-1}.
  7. Ex 3.7
    Determine the current in each branch of the network shown in Fig. 3.20:
  8. Ex 3.8
    A storage battery of emf 8.0 V8.0\,\text{V} and internal resistance 0.5 Ω0.5\,\Omega is being charged by a 120 V120\,\text{V} dc supply using a series resistor of 15.5 Ω15.5\,\Omega. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?
  9. Ex 3.9
    The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5×1028 m−38.5 \times 10^{28}\,\text{m}^{-3}. How long does an electron take to drift from one end of a wire 3.0 m3.0\,\text{m} long to its other end? The area of cross-section of the wire is 2.0×10−6 m22.0 \times 10^{-6}\,\text{m}^2 and it is carrying a current of 3.0 A3.0\,\text{A}.