Physics · Textbook solutions

Current Electricity

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 47 questions

9. Current Electricity — worked examples

10 q

Solved Examples

Worked · 10
  1. Solved Ex.9.1
    Figure shows currents in a part of electrical circuit. Find the current XX?
  2. Solved Ex.9.2
    Two batteries of 7 volt and 13 volt and internal resistances 1 ohm and 2 ohm respectively are connected in parallel with a resistance of 12 ohm. Find the current through each branch of the circuit and the potential difference across 12-ohm resistance.
  3. Solved Ex.9.3
    For the given network, find the current through 4 ohm and 3 ohm. Assume that the cells have negligible internal resistance.
  4. Solved Ex.9.4
    At what value should the variable resistor Q be set in the circuit such that the bridge is balanced? If the source voltage is 30 V find the value of the output voltage across XYXY, when the bridge is balanced.
  5. Solved Ex.9.5
    Two resistances 2 ohm and 3 ohm are connected across the two gaps of the metre bridge as shown in figure. Calculate the current through the cell when the bridge is balanced and the specific resistance of the material of the metre bridge wire. Given the resistance of the bridge wire is 1.49 ohm and its diameter is 0.12 cm.
  6. Solved Ex.9.6
    In an experiment to determine the internal resistance of a cell of emf 1.5 V, the balance point in the open cell condition is at 76.3 cm. When a resistor of 9.5 ohm is used in the external circuit of the cell the balance point shifts to 64.8 cm of the potentiometer wire. Determine the internal resistance of the cell.
  7. Solved Ex.9.7
    A galvanometer has a resistance of 100 Ω\Omega and its full scale deflection current is 100 μ\muA. What shunt resistance should be added so that the ammeter can have a range of 0 to 10 mA?
  8. Solved Ex.9.8
    What is the value of the shunt resistance that allows 20% of the main current through a galvanometer of 99 Ω\Omega?
  9. Solved Ex.9.9
    A galvanometer has a resistance of 25 Ω\Omega and its full scale deflection current is 25 μ\muA. What resistance should be added to it to have a range of 0 - 10 V?
  10. Solved Ex.9.10
    A galvanometer has a resistance of 40 Ω\Omega and a current of 4 mA is needed for a full scale deflection. What is the resistance and how is it to be connected to convert the galvanometer (a) into an ammeter of 0.4 A range and (b) into a voltmeter of 0.5 V range?

Exercises

37 q

Choose the correct option

Practice · 6
  1. Choose the correct option.
    Ex Q.1 (i)
    Kirchhoff's first law, i.e., ΣI=0\Sigma I = 0 at a junction, deals with the conservation of
    1. A.
      charge
    2. B.
      energy
    3. C.
      momentum
    4. D.
      mass
  2. Ex Q.1 (ii)
    When the balance point is obtained in the potentiometer, a current is drawn from
    1. A.
      both the cells and auxiliary battery
    2. B.
      cell only
    3. C.
      auxiliary battery only
    4. D.
      neither cell nor auxiliary battery
  3. Ex Q.1 (iii)
    In the following circuit diagram, an infinite series of resistances is shown. Equivalent resistance between points A and B is
    1. A.
      infinite
    2. B.
      zero
    3. C.
      2 Ω2\ \Omega
    4. D.
      1.5 Ω1.5\ \Omega
  4. Ex Q.1 (iv)
    Four resistances 10 Ω10\ \Omega, 10 Ω10\ \Omega, 10 Ω10\ \Omega and 15 Ω15\ \Omega form a Wheatstone's network. What shunt is required across 15 Ω15\ \Omega resistor to balance the bridge
    1. A.
      10 Ω10\ \Omega
    2. B.
      15 Ω15\ \Omega
    3. C.
      20 Ω20\ \Omega
    4. D.
      30 Ω30\ \Omega
  5. Ex Q.1 (v)
    A circular loop has a resistance of 40 Ω40\ \Omega. Two points P and Q of the loop, which are one quarter of the circumference apart are connected to a 24 V battery, having an internal resistance of 0.5 Ω0.5\ \Omega. What is the current flowing through the battery.
    1. A.
      0.5 A
    2. B.
      1A
    3. C.
      2A
    4. D.
      3A
  6. Ex Q.1 (vi)
    To find the resistance of a gold bangle, two diametrically opposite points of the bangle are connected to the two terminals of the left gap of a metre bridge. A resistance of 4 Ω4\ \Omega is introduced in the right gap. What is the resistance of the bangle if the null point is at 20 cm from the left end?
    1. A.
      2 Ω2\ \Omega
    2. B.
      4 Ω4\ \Omega
    3. C.
      8 Ω8\ \Omega
    4. D.
      16 Ω16\ \Omega

Answer in brief

Practice · 13
  1. Answer in brief.
    Ex Q.2 (i)
    Define or describe a Potentiometer.
  2. Ex Q.2 (ii)
    Define Potential Gradient.
  3. Ex Q.2 (iii)
    Why should not the jockey be slided along the potentiometer wire?
  4. Ex Q.2 (iv)
    Are Kirchhoff's laws applicable for both AC and DC currents?
  5. Ex Q.2 (v)
    In a Wheatstone's meter-bridge experiment, the null point is obtained in middle one third portion of wire. Why is it recommended?
  6. Ex Q.2 (vi)
    State any two sources of errors in meter-bridge experiment. Explain how they can be minimized.
  7. Ex Q.2 (vii)
    What is potential gradient? How is it measured? Explain.
  8. Ex Q.2 (viii)
    On what factors does the potential gradient of the wire depend?
  9. Ex Q.2 (ix)
    Why is potentiometer preferred over a voltmeter for measuring emf?
  10. Ex Q.2 (x)
    State the uses of a potentiometer.
  11. Ex Q.2 (xi)
    What are the disadvantages of a potentiometer?
  12. Ex Q.2 (xii)
    Distinguish between a potentiometer and a voltmeter.
  13. Ex Q.2 (xiii)
    What will be the effect on the position of zero deflection if only the current flowing through the potentiometer wire is (i) increased (ii) decreased.

Solve the following

Practice · 18
  1. Ex Q.3
    Obtain the balancing condition in case of a Wheatstone's network.
  2. Ex Q.4
    Explain with neat circuit diagram, how you will determine the unknown resistance by using a meter-bridge.
  3. Ex Q.5
    Describe Kelvin's method to determine the resistance of a galvanometer by using a meter bridge.
  4. Ex Q.6
    Describe how a potentiometer is used to compare the emfs of two cells by connecting the cells individually.
  5. Ex Q.7
    Describe how a potentiometer is used to compare the emfs of two cells by combination method.
  6. Ex Q.8
    Describe with the help of a neat circuit diagram how you will determine the internal resistance of a cell by using a potentiometer. Derive the necessary formula.
  7. Ex Q.9
    On what factors does the internal resistance of a cell depend?
  8. Ex Q.10
    A battery of emf 4 volt and internal resistance 1 Ω1\ \Omega is connected in parallel with another battery of emf 1 V and internal resistance 1 Ω1\ \Omega (with their like poles connected together). The combination is used to send current through an external resistance of 2 Ω2\ \Omega. Calculate the current through the external resistance.
  9. Ex Q.11
    Two cells of emf 1.5 Volt and 2 Volt having respective internal resistances of 1 Ω1\ \Omega and 2 Ω2\ \Omega are connected in parallel so as to send current in same direction through an external resistance of 5 Ω5\ \Omega. Find the current through the external resistance.
  10. Ex Q.12
    A voltmeter has a resistance 30 Ω30\ \Omega. What will be its reading, when it is connected across a cell of emf 2 V having internal resistance 10 Ω10\ \Omega?
  11. Ex Q.13
    A set of three coils having resistances 10 Ω10\ \Omega, 12 Ω12\ \Omega and 15 Ω15\ \Omega are connected in parallel. This combination is connected in series with series combination of three coils of the same resistances. Calculate the total resistance and current through the circuit, if a battery of emf 4.1 Volt is used for drawing current.
  12. Ex Q.14
    A potentiometer wire has a length of 1.5 m and resistance of 10 Ω10\ \Omega. It is connected in series with the cell of emf 4 Volt and internal resistance 5 Ω5\ \Omega. Calculate the potential drop per centimeter of the wire.
  13. Ex Q.15
    When two cells of emfs. ε1\varepsilon_1 and ε2\varepsilon_2 are connected in series so as to assist each other, their balancing length on a potentiometer is found to be 2.7 m. When the cells are connected in series so as to oppose each other, the balancing length is found to be 0.3 m. Compare the emfs of the two cells.
  14. Ex Q.16
    The emf of a cell is balanced by a length of 120 cm of potentiometer wire. When the cell is shunted by a resistance of 10 Ω10\ \Omega, the balancing length is reduced by 20 cm. Find the internal resistance of the cell.
  15. Ex Q.17
    A potential drop per unit length along a wire is 5×10−35 \times 10^{-3} V/m. If the emf of a cell balances against length 216 cm of this potentiometer wire, find the emf of the cell.
  16. Ex Q.18
    The resistance of a potentiometer wire is 8 Ω8\ \Omega and its length is 8 m. A resistance box and a 2 V battery are connected in series with it. What should be the resistance in the box, if it is desired to have a potential drop of 1 μ1\ \muV/mm?
  17. Ex Q.19
    Find the equivalent resistance between the terminals F and B in the network shown in the figure below given that the resistance of each resistor is 10 ohm.
  18. Ex Q.20
    A voltmeter has a resistance of 100 Ω100\ \Omega. What will be its reading when it is connected across a cell of emf 2 V and internal resistance 20 Ω20\ \Omega?