CHAPTER -3 CURRENT ELECTRICITY

A room has AC run for 5 hours a day at a voltage of 220V. The
wiring of the room consists of Cu of 1 mm radius and a length of
10 m. Power consumption per day is 10 commercial units. What
fraction of it goes in the joule heating in wires? What would happen
if the wiring is made of aluminium of the same dimensions?

Suppose there is a circuit consisting of only resistances and
batteries. Suppose one is to double (or increase it to n-times) all
voltages and all resistances. Show that currents are unaltered.
Do this for circuit of Example 3.7 in the NCERT Text Book for
Class XII.

Two conductors are made of the same material and have the same
length. Conductor A is a solid wire of diameter 1mm. Conductor B
is a hollow tube of outer diameter 2mm and inner diameter 1mm.
Find the ratio of resistance RA to RB.

Let there be n resistors R1 . ..........Rn with Rmax = max (R1......... Rn)
and Rmin = min {R1 ..... Rn}. Show that when they are connected in
parallel, the resultant resistance RP< Rmin and when they are
connected in series, the resultant resistance RS > Rmax. Interpret
the result physically.

First a set of n equal resistors of R each are connected in series to
a battery of emf E and internal resistance R. A current I is observed
to flow. Then the n resistors are connected in parallel to the same
battery. It is observed that the current is increased 10 times. What
is ‘n’?

A cell of emf E and internal resistance r is connected across an
external resistance R. Plot a graph showing the variation of P.D.
across R, verses R.

Power P is to be delivered to a device via transmission
cables having resistance RC. If V is the voltage across R
and I the current through it, find the power wasted
and how can it be reduced.

Why are alloys used for making standard resistance coils?

For wiring in the home, one uses Cu wires or Al wires. What
considerations are involved in this?

What is the advantage of using thick metallic strips to join wires
in a potentiometer?

What are the advantages of the null-point method in a Wheatstone
bridge? What additional measurements would be required to
calculate Run  known by any other method?

The relaxation time τ is nearly independent of applied E field
whereas it changes significantly with temperature T. First fact is
(in part) responsible for Ohm’s law whereas the second fact leads
to variation of ρ with temperature. Elaborate why?

Is the motion of a charge across junction momentum conserving?
Why or why not?

Two wires X, Y have the same resistivity, but their cross-sectional areas are in the ratio 2 : 3 and

lengths in the ratio 1 : 2. They are first connected in series and then in parallel to a d.c. source.

Find out the ratio of the drift speeds of the electrons in the two wires for the two cases.

Two conducting wires X and Y of same diameter but different materials are joined in series across

a battery. If the number density of electrons in X is twice that in Y, find the ratio of drift velocity

of electrons in the two wires.

Two heating elements of resistance R1 and R2 when operated at a constant supply of voltage, V,

consume powers P1 and P2 respectively. Deduce the expressions for the power of their

combination when they are, in turn, connected in (i) series and (ii) parallel across the same voltage

supply.

Write principle of potentiometer.

Two wires of equal length, one of copper and the other of manganin have the same resistance.

Which wire is thicker?

Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel with

each other across an external resistance R. What is the current through this resistance?

Answer the following :

(a) Why are the connections between the resistors in a meter bridge made of thick copper strips ?

(b) Why is it generally preferred to obtain the balance point in the middle of the meter bridge wire ?

(c) Which material is used for the meter bridge wire and why ? 

A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a graph showing variation of terminal voltage ‘V’ of the cell versus the current ‘I’. Using the plot, show how the emf of the cell and its internal resistance can be determined.

Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 x 10^–7 m2 carrying a current of 1.5 A. Assume the density of conduction electrons to be 9 x 10²⁸ m^–3.

Figure 3.35 shows a 2.0 V potentiometer used for the determination of internal resistance of a 1.5 V cell. The balance point of the cell in open circuit is 76.3 cm. When a resistor of 9.5 Ω 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.

Figure 3.34 shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 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 ÃŽÂµ?

Figure 3.33 shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Ω 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 up to 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 kΩ 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 ÃŽÂµ and the balance point found similarly, turns out to be at 82.3 cm length of the wire.

(a) What is the value ÃŽÂµ ?

(b) What purpose does the high resistance of 600 kΩ have?

(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 a thermo-couple)? If not, how will you modify the circuit?

Determine the current drawn from a 12 V supply with internal resistance 0.5 Ω by the infinite network shown in Fig. 3.32. Each resistor has 1 Ω resistance.

(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 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (i) (11/3) Ω (ii) (11/5) Ω, (iii) 6 Ω, (iv) (6/11) Ω?

(c) Determine the equivalent resistance of networks shown in Fig. 3.31.

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).

Answer the following questions:

(a) A steady current flows in a metallic conductor of non-uniform 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?

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

Current A	Voltage V	Current A	Voltage V
0.2	3.94	3.0	59.2
0.4	7.87	4.0	78.8
0.6	11.8	5.0	98.6
0.8	15.7	6.0	118.5
1.0	19.7	7.0	138.2
2.0	39.4	8.0	158.0

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. (ÃÂAl = 2.63 x 10-8 ÃŽÂ© m, ÃÂCu = 1.72 x 10-8 ÃŽÂ© m, Relative density of Al = 2.7, of Cu = 8.9.)

(a) Six lead-acid type of secondary cells each of emf 2.0 V and internal resistance 0.015 Ω are joined in series to provide a supply to a resistance of 8.5 Ω. 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 of 380 Ω. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?

The earth's surface has a negative surface charge density of 10-9 C m-2. The potential difference of 400 kV between the top of the atmosphere and the surface results (due to the low conductivity of 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.)

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 10-6 m2 and it is carrying a current of 3.0 A.

In a potentiometer arrangement, a cell of emf 1.25 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?

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

(a) In a metre bridge [Fig. 3.27], the balance point is found to be at 39.5 cm from the end A, when the resistor Y is of 12.5 Ω. 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?

Determine the current in each branch of the network shown in fig 3.30:

Aheating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds toa 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 °C -1.

A silver wire has a resistance of 2.1 Ω at 27.5 °C, and a resistance of 2.7 Ω at 100 °C. Determine the temperature coefficient of resistivity of silver.

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 Ω. What is the resistivity of the material at the temperature of the experiment?

At room temperature (27.0 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the material of the resistor is 

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

(b) If the combination is connected to a battery of emf 20 V and negligible internal resistance, determine the current through each resistor, and the total current drawn from the battery.

(a) Three resistors 1 Ω, 2 Ω, and 3 Ω 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.

A battery of emf 10 V and internal resistance 3 Ω 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?

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