### Exercise

**Question 1. The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Q what is the maximum current that can be drawn from the battery?**

**Question 2. A battery of emf 10 V and internal resistance 3Q is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?**

**Question 3. (a) Three resistors of resistances 1Q ,2Q and 3Q are combined in series. What is the total resistance of the combination?**

**(b) If the combination is connected to a battery of emf 12 V and negligible internal resistance, obtain the potential drop across each resistor.**

**Question 4. (a) Three resistors of 2Q , 4Q and 5Q are combined in parallel. What is the total resistance of the combination?**

**(b) If the combination is connected to a battery of emf20 V and negligible internal resistance then determine the current through each resistor, and the total current drawn from the battery.**

**Note:** Refer Chapter at a Glance (10)

**Question 5. At room temperature (27°C) the resistance of a heating element is 100n. What is the temperature of the element if the resistance is found to be 117 n given that the temperature coefficient of the material of the resistor is 1.70 X 10-4 oc-l.**

**Note: **Refer Chapter at a Glance (10)

**Question 6. A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 x 10-7 m2, and its resistance is measured to be 5.0 Q. What is the resistivity of the material?**

**Question 7. A silver wire has a resistance of 2.1 n at 27.5°C, and a resistance of 2.7 Q at 100°C. Determine the temperature coefficient of resistivity of silver.**

**Question 8. A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0°C? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 X 10-4 oc-l.**

**Question 9. Determine the current in each branch of the network shown in Figure.**

**Note: **Use Kirchoff’s voltage law and find the current distribution.

**Question 10. (a) In a metre bridge, the balance point is found to be at 39.5 cm from the end A. When the resistor Y is of12.5 n determine the resistance of X. Why are the connections between resistors in a Wheatstone or meter bridge made of thick copper strips?(b) Determine the balance point of the bridge above if X and Y are interchanged.(c) What happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the galvanometer show any current?**

**Question 11. A storage battery of emf 8.0 V and internal resistance 0.5 n is being charged by a 120 V D.C. supply using a series resistor of 15.5 n .What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?**

**Question 12. In a potentiometer arrangement, a cell of emfl.25 V gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm. what is the emf of the second cell?**

**Question 13. The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 x 1028 m-3• How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross section of the wire is 2.0 x 10—0 m2 and it is carrying a current of 3.0 A.**

### Additional NCERT Exercise

**Question 14. The earth’s surface has a negative surface charge density of 10-6 m-2• The potential difference of 400 kV between the top of the atmosphere and the surface results (due to the low conductivity to the lower atmosphere) in a current of only 1800 A over the entire globe. If there were no mechanism of sustaining atmospheric electric field, how much time (roughly) would be required to neutralise the earth’s surface? (This never happens in practice because there is a mechanism to replenish electric charges, namely the continual thunderstorms and lightning in different parts of the globe). (Radius of earth= 6.37 x 106 m.)**

**Question 15. (a) Six lead-acid type of secondary cells each of emf2.0 V and internalresistance 0.015 Q are joined in series to provide a supply to a resistance of 8.5 Q. What are the current drawn from the supply and its terminal voltage?(b) A secondary cell after long use has an emf of 1.9 V and a large internal resistance 380 Q. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?**

**Question 16. Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables.**

**Question 17. What conclusion can you draw from the following observations on a resistor made of alloy manganin?**

**Note:** Find the resistance to see if the voltage varries linearly with the resistance

**Question 18. Answer the following questions:**

**(a) A steady current flows in a metallic conductor of nonuniform cross section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?****(b) Is Ohm’s law universally applicable for all conducting elements? If****not, give examples of elements which do not obey Ohm’s law.****(c) A low voltage supply from which one needs high currents must have very low internal resistance. Why?****(d) A high tension (HT) supply of say, 6 kV must have a very large internal resistance. Why?**

**Sol. (a)** Only current (because it is given to be steady!). The rest depends on the area of cross-section inversely.**(b)** No, examples of non-ohmic elements vacuum diode, semiconductor diode etc.**(c)** Because the maximum current drown from source is equal to sir.**(d) **Because, if the circuit is shorted (accidentally), the current drawn will exceed safety limits, if internal resistance is not large.

**Question 19. Choose the correct alternative:(a) Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.(b) Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.(c) The resistivity of the alloy manganin is nearly independent of/ increases rapidly with increase of temperature.(d) The resistivity of a typical insulator (e.g., amber) is greater than that of a metal by a factor of the order of (1022/103).**

**Sol.** (a) greater

(b) lower

(c) nearly independent of,

(d) 1022

**Note: **Some materials such as Nichrome, Manganin etc show a weak dependence of resistivity with temperature.

**Question 20. (a) Given n resistors each of resistance R, how will you combine them to get the (i) maximum (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?**

**(b) Given the resistances of 1 n , 2n , 3n , how will be combine them to get an equivalent resistance of (i) (11/3) n (ii) (11/5) n, (iii) 6 n(iv) (6/11) Q?**

**Question 21. Determine the current drawn from a 12 V supply with internal resistance0.50 by the infinite network shown in fig. Each resistor has 10 resistance.**

**Note:** Observe carefully that pattern is repeated and chain is infinite. Draw the equivalent circuit to find the equivalent resistance.

**Question 22. Figure shows a potentiometer with a cell of2.0 V and internal resistance0.40 n maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 kn is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf E and the balance point found similarly, turns out to be at 82.3 cm length of the wire.**

**(c) Is the balance point affected by this high resistance?(d) Is the balance point affected by the internal resistance of the driver cell?(e) Would the method work in the above situation if the driver cell of the potentiometer had an emf of 1.0 V instead of 2.0 V?(f) Would the circuit work well for determining an extremely small emf, say of the order of a few mV (such as the typical emf of the thermo couple)? If not, how will you modify the circuit?**

**(b)** To reduce the current through the galvanometer when the movable contact is far from the balance point.**(c)** No.**(d)** No.**(e)** No. If E is greater than the emf of the drive cell of the potentiometer, there will be no balance point on the wire AB.**(f)**The circuit, as it is, would be unsuitable because the balance point (for s of the order a few mV) will be very close to the end A and the percentage error in measurement will be very large. The circuit is modified by putting a suitable resistor R in series with the wire AB so that potential drop across AB is only slightly greater than the emf to be measured. Then the balance point will be at larger length of the wire and the percentage error will be much smaller.

**Question 23. Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 n is found to be 58.3 cm, while that with the unknown resistance Xis 68.5 cm. Determine the value of X. What might you do if you failed to find a balance point with the given cell of emf E?**

**Question 24. Figure shows a 2.0 V potentiometer used for the determination of internal resistance of a 1.5 V cell. The balance point of cell in open circuit is 76.3 cm. When a resistor of 9.5 Q is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. Determine the internal resistance of the cell.**

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