Download Electricity(num)

Pavitra Gupta 9312281591
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Pavitra Gupta 9312281591
CURRENT ELECTRICTY (Numericals)
In hydrogen atom, the electron moves in an orbit of radius 5 x 10-11 m with a speed of 2.2 x 106 m/s. Find
the equivalent current.
[1.12 mA]
A solution of NaCl discharges 6.1 x 1016 Na+ ions and 4.6 x 1016 Cl- ions in 2 seconds. Find the current
passing through the solution.
[8.56 x 10-3 A]
The number density of free electrons in a copper conductor is 8.5 × 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 × 10-6 m2 and it is carrying a current of 3.0 A.
[7.5 hour]
A wire of resistance R = 4 Ω is stretched, so that its radius decreases to, by a factor n = 5, calculate its
new resistance.
[2.5 Ω]
A wire of resistance 5 Ω is drawn out such that its length increases by twice its original length. Calculate
its new resistance.
[45 Ω]
Find the resistance of a hollow cylindrical pipe of length 1 m whose inner and outer radii are 10 cm and
20 cm respectively. The resistivity of material is 2 x 10-8 Ωm.
[2.l x l0-7 Ω]
Calculate the relaxation time and mean free path at room temperature ( 27°C ), if the number of free
electrons per unit volume is 8.5 x 1028 /m3 and resistivity is 1.7 x 10-8 Ωm. Given that Boltzmann’s
constant = 1.38 x 10-23 J/K.
[2.46 x 10-14 s ; 28.7 Å]
The sequence of bands marked on a carbon resistor is brown, black, brown and gold. Find the value of
the resistance?
[100 Ω ± 5%]
A carbon resistance of 47 kΩ is to be marked with rings of different colours for its identification. Write
the sequence of colours.
[ yellow, violet and orange]
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 × 10-4 °C-1.
[867.2 C]
A parallel combination of three resistors take a current of 7.5 A from a 30 V supply. If the two resistors
are 10 Ω and 12 Ω, find the third one.
[15 Ω]
(a) Calculate the equivalent resistance between A & B in the figures (i) to (iv).
(b) Calculate resistance between A & B and A & C in figure (v)
(i)
(ii)
(iii)
(iv)
(v)
[9.6Ω, 40/3 Ω, 7.5 Ω, 2 Ω, 27.5 Ω, 30 Ω]
Q.13
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Calculate the current
shown by ammeter A.
[3.6 A]
An infinite ladder net work of resistance is constructed with 1 Ω and
2 Ω resistances, as shown in Figure . The 6 V battery between A and
B has negligible internal resistance.
(i) Show that the effective resistance between A and B is 2Ω.
(ii) What is the current that passes through the 2 Ω resistance nearest to the battery?
Pavitra Gupta 9312281591
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[1.5 A]
Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
Q.15 The total resistance of two resistors when connected in series is 9 Ω and when connected in parallel, their
total resistance becomes 2 Ω. Find the value of each resistance.
[3Ω, 6Ω]
Q.16 A battery of e.m.f. 6.6 V can supply a current of 3 A through a resistance of 1.8 Ω. What current will it
supply through another resistance of 2.9 Ω.? Also calculate internal resistance of the battery. [ 2A, 0.4Ω]
Q.17 A battery of emf, E and internal resistance r gives a current of 0.4 A with an external resistor of 12 ohm,
and a current of 0.25 A with an external resistor of 20 ohm. Calculate (1) internal resistance and (ii) emf
of the battery.
[4/3 Ω, 16/3 V]
Q.18 A cell is connected in series with ammeter; a resistor and key K. A voltmeter is connected in parallel to
cell. When key K is open, the voltmeter reads 1.5 V. When key K is closed, the voltmeter reads 1.35 V
while ammeter reads 10 A. Find the e.m.f. and internal resistance of the cell.
[1.5 V, 0.015 Ω]
Q.19 You are given several identical resistances each of value R = 10 Ω and each capable of carrying a
maximum current of one ampere. It is required to make a suitable combination of these resistances of 5Ω
which can carry a current of 4 ampere. Find the minimum number of resistances required.
[8]
Q.20 Two identical cells of emf 1.5 V each joined in parallel provide supply to an external circuit consisting of
two resistors of 17 Ω each joined in parallel. A voltmeter reads the terminal voltage of cells to be 1.4 V.
What is the internal resistance of each cell?
[1.21 Ω]
Q.21 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?
[1.4 A, 11.9 V]
Q.22 A letter ‘A’ consists of uniform wire of resistance 1 Ω/cm. The sides of letter are each 20 cm long and the
cross – piece joining the mid points of two sides is 10 cm long. Find resistance of letter between two ends
of the legs.
[26.67 Ω]
Q.23
Determine the current in each branch of the network
shown in the figure:
Q.24
Determine the current through BD, if current through the cell is 2 A in the given figure.
Q.25
[0.5 A]
Calculate the current in DC and
voltage across AB in the figure.
[16/63 A, 3.38V]
Q.26
In the given circuit, E, F, G and H are cells of emfs 2 V, 1 V, 3 V and 1 V;
and their internal resistances are 2 Ω, 1 Ω, 3 Ω and 1 Ω respectively. Find
(i) potential difference between B and D.
(ii) p.d. across each cells G and H.
[0.154 V, 1.61 V, 1.46 V]
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Find the resistance of the circuit between A and B, if each resistance is r.
[8r/7]
Two cells of emfs 4.5 V and 6.0 V having internal resistances 6 Ω and 3 Ω respectively have their
negative terminals joined by a wire of 18 Ω and positive terminals by a wire of 12 Ω resistances. A wire
of 24 Ω connects middle points of these wires. Find the potential difference at the ends of third wire.
[3.78 V]
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Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
Q.29 Find the value of the unknown resistance X, in the following circuit,
if no current flows through the section AO. Also calculate
the current drawn by the circuit from the battery of emf 6 V
and negligible internal resistance.
[X = 6 Ω, I =1 A]
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Pavitra Gupta 9312281591
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.
[1.68 Ω]
AB is one metre long uniform wire of 10 Ω resistance.
The other data are shown in the circuit diagram given: Calculate
(i) Potential gradient along AB, and
(ii) length AO of the wire, when the galvanometer
shows no deflection.
[(i) 0.8 V/m (ii) AO = 37.5 cm]
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Q.39
Find the value of unknown resistance X and the current drawn by
the circuit from the battery, if no current flows through the
galvanometer. Assume the resistance per unit length
of the wire AB to be 0.01 Ω/cm.
[3 Ω, I = 2.8 A]
In the circuit diagram given below AB is a uniform wire of
resistance 10 ohm and length one metre. It is connected to a series
arrangement of cell E1 of emf 2.0 V and negligible internal
resistance and a resistor R. Terminal A is also connected to an
electrochemical cell E2 of emf 100 mV and a galvanometer G.
In this set-up a balancing point is obtained at 40 cm mark from A.
Calculate the resistance of R.
If E2 were to have an emf of 300 mV, where will you expect the balancing point to be?
[70 Ω]
Two bulbs are 100 W and 500 W. Which bulb will glow brighter, when they are connected in (i) series
(ii) parallel?
An electric bulb is marked 100 W; 230 V. If the supply voltage drops to 115 V, what is the heat and light
energy produced by the bulb in 20 minutes?
[30 kJ]
The maximum power rating of 20 Ω resistor is 2 kW. Would you connect this resistor directly across a
300 V supply? Explain your answer.
An electric power station of 100 MW transmits power through long and thin cables to a distant load.
Which of the 2 modes of transmission would result in lesser wastage: Power transmission at (i) 20000 V
or (ii) 200 V?
The 2.0 Ω resistor shown in Figure is dipped into a calorimeter
containing water. The heat capacity of the calorimeter together
with water is 2000 J/K.
(a) If the circuit is active for 30 minutes, what would be the rise
in temperature of the water?
(b) If the 6.0 Ω resistor gets burnt, what would be the rise in temperature
of the water in next 30 minutes?
[5.8°C, 7.2°C]
A heater coil is rated 100 W, 200 V. It is cut into two identical parts.
Both parts are connected together in parallel, to the same source of
200 V. Calculate the energy liberated per second in the new combination.
Pavitra Gupta 9312281591
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[400 J]
Pavitra Gupta 9312281591