Physics · Textbook solutions

Electric Current Through Conductors

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 32 questions

11. Electric Current Through Conductors — worked examples

8 q

Solved Examples

Worked · 8
  1. Solved Ex.11.1
    A metallic wire of diameter 0.02 m contains 102810^{28} free electrons per cubic meter. Find the drift velocity for free electrons, having an electric current of 100 amperes flowing through the wire. (Given : charge on electron =1.6×10−19= 1.6 \times 10^{-19} C)
  2. Solved Ex.11.2
    A copper wire of radius 0.6 mm carries a current of 1 A. Assuming the current to be uniformly distributed over a cross sectional area, find the magnitude of current density.
  3. Solved Ex.11.3
    A Flashlight uses two 1.5 V batteries to provide a steady current of 0.5 A in the filament. Determine the resistance of the glowing filament.
  4. Solved Ex.11.4
    An electric heater takes 6 A current from a 230 V supply line, calculate the power of the heater and electric energy consumed by it in 5 hours.
  5. Solved Ex.11.5
    Calculate i) total resistance and ii) total current in the following circuit. R1=3 ΩR_{1} = 3\ \Omega, R2=6 ΩR_{2} = 6\ \Omega, R3=5 ΩR_{3} = 5\ \Omega, V=14V = 14 V
  6. Solved Ex.11.6
    Calculate the resistance per metre, at room temperature, of a constantan (alloy) wire of diameter 1.25 mm. The resistivity of constantan at room temperature is 5.0×10−7 Ω5.0 \times 10^{-7}\ \Omegam.
  7. Solved Ex.11.7
    A piece of platinum wire has resistance of 2.5 Ω2.5\ \Omega at 0∘0^{\circ}C. If its temperature coefficient of resistance is 4×10−3/∘4 \times 10^{-3}/^{\circ}C. Find the resistance of the wire at 80∘80^{\circ}C.
  8. Solved Ex.11.8
    A network of resistors is connected to a 15 V battery with internal resistance 1 Ω1\ \Omega as shown in the circuit diagram. Calculate (i) The equivalent resistance, (ii) Current in each resistor, (iii) Voltage drops VABV_{AB}, VBCV_{BC} and VDCV_{DC}.

Exercises

24 q

Choose correct alternative

Practice · 8
  1. Choose correct alternative
    Ex Q.1 (i)
    You are given four bulbs of 25 W, 40 W, 60 W and 100 W of power, all operating at 230 V. Which of them has the lowest resistance?
    1. A.
      25 W
    2. B.
      40 W
    3. C.
      60 W
    4. D.
      100 W
  2. Ex Q.1 (ii)
    Which of the following is an ohmic conductor?
    1. A.
      transistor
    2. B.
      vacuum tube
    3. C.
      electrolyte
    4. D.
      nichrome wire
  3. Ex Q.1 (iii)
    A rheostat is used
    1. A.
      to bring on a known change of resistance in the circuit to alter the current
    2. B.
      to continuously change the resistance in any arbitrary manner and there by alter the current
    3. C.
      to make and break the circuit at any instant
    4. D.
      neither to alter the resistance nor the current
  4. Ex Q.1 (iv)
    The wire of length LL and resistance RR is stretched so that its radius of cross-section is halved. What is its new resistance?
    1. A.
      5R5R
    2. B.
      8R8R
    3. C.
      4R4R
    4. D.
      16R16R
  5. Ex Q.1 (v)
    Masses of three pieces of wires made of the same metal are in the ratio 1:3:5 and their lengths are in the ratio 5:3:1. The ratios of their resistances are
    1. A.
      1:3:5
    2. B.
      5:3:1
    3. C.
      1:15:125
    4. D.
      125:15:1
  6. Ex Q.1 (vi)
    The internal resistance of a cell of emf 2 V is 0.1 Ω0.1\ \Omega it is connected to a resistance of 0.9 Ω0.9\ \Omega. The voltage across the cell will be
    1. A.
      0.5 V
    2. B.
      1.8 V
    3. C.
      1.95 V
    4. D.
      3V
  7. Ex Q.1 (vii)
    100 cells each of emf 5 V and internal resistance 1 Ω1\ \Omega are to be arranged so as to produce maximum current in a 25 Ω25\ \Omega resistance. Each row contains equal number of cells. The number of rows should be
    1. A.
      2
    2. B.
      4
    3. C.
      5
    4. D.
      100
  8. Ex Q.1 (viii)
    Five dry cells each of voltage 1.5 V are connected as shown in diagram What is the overall voltage with this arrangement?
    1. A.
      0V
    2. B.
      4.5V
    3. C.
      6.0V
    4. D.
      7.5V

Give reasons / short answers

Practice · 2
  1. Give reasons / short answers
    Ex Q.2 (i)
    In given circuit diagram two resistors are connected to a 5V supply. a] Calculate potential difference across the 8 Ω8\ \Omega resistor. b] A third resistor is now connected in parallel with 6 Ω6\ \Omega resistor. Will the potential difference across the 8 Ω8\ \Omega resistor the larger, smaller or the same as before? Explain the reason for your answer.
  2. Ex Q.2 (ii)
    Prove that the current density of a metallic conductor is directly proportional to the drift speed of electrons.

Answer the following questions

Practice · 2
  1. Answer the following questions.
    Ex Q.3 (i)
    Distinguish between Ohmic and non-ohmic substances; explain with the help of example.
  2. Ex Q.3 (ii)
    DC current flows in a metal piece of non-uniform cross-section. Which of these quantities remains constant along the conductor: current, current density or drift speed?

Solve the following problems

Practice · 12
  1. Solve the following problems.
    Ex Q.4 (i)
    What is the resistance of one of the rails of a railway track 20 km long at 20∘20^{\circ}C? The cross section area of rail is 25 cm2^{2} and the rail is made of steel having resistivity at 20∘20^{\circ}C as 6×10−8 Ω6 \times 10^{-8}\ \Omega m.
  2. Ex Q.4 (ii)
    A battery after a long use has an emf 24 V and an internal resistance 380 Ω380\ \Omega. Calculate the maximum current drawn from the battery? Can this battery drive starting motor of car?
  3. Ex Q.4 (iii)
    A battery of emf 12 V and internal resistance 3 Ω3\ \Omega is connected to a resistor. If the current in the circuit is 0.5 A, a] Calculate resistance of resistor. b] Calculate terminal voltage of the battery when the circuit is closed.
  4. Ex Q.4 (iv)
    The magnitude of current density in a copper wire is 500 A/cm2^{2}. If the number of free electrons per cm3^{3} of copper is 8.47×10228.47 \times 10^{22} calculate the drift velocity of the electrons through the copper wire (charge on an e=1.6×10−19e = 1.6 \times 10^{-19} C)
  5. Ex Q.4 (v)
    Three resistors 10 Ω10\ \Omega, 20 Ω20\ \Omega and 30 Ω30\ \Omega are connected in series combination. i] Find equivalent resistance of series combination. ii] When this series combination is connected to 12V supply, by neglecting the value of internal resistance, obtain potential difference across each resistor.
  6. Ex Q.4 (vi)
    Two resistors 1k Ω1\text{k}\ \Omega and 2k Ω2\text{k}\ \Omega are connected in parallel combination. i] Find equivalent resistance of parallel combination ii] When this parallel combination is connected to 9 V supply, by neglecting internal resistance calculate current through each resistor.
  7. Ex Q.4 (vii)
    A silver wire has a resistance of 4.2 Ω4.2\ \Omega at 27∘27^{\circ}C and resistance 5.4 Ω5.4\ \Omega at 100∘100^{\circ}C. Determine the temperature coefficient of resistance.
  8. Ex Q.4 (viii)
    A 6m long wire has diameter 0.5 mm. Its resistance is 50 Ω50\ \Omega. Find the resistivity and conductivity.
  9. Ex Q.4 (ix)
    Find the value of resistances for the following colour code. 1. Blue Green Red Gold 2. Brown Black Red Silver 3. Red Red Orange Gold 4. Orange White Red Gold 5. Yellow Violet Brown Silver
  10. Ex Q.4 (x)
    Find the colour code for the following value of resistor having tolerance ±10%\pm 10\% a) 330 Ω330\ \Omega b) 100 Ω100\ \Omega c) 47k Ω47\text{k}\ \Omega d) 160 Ω160\ \Omega e) 1k Ω1\text{k}\ \Omega
  11. Ex Q.4 (xi)
    A current 4A flows through an automobile headlight. How many electrons flow through the headlight in a time 2hrs.
  12. Ex Q.4 (xii)
    The heating element connected to 230V draws a current of 5A. Determine the amount of heat dissipated in 1 hour (J = 4.2 J/cal.).