This chapter deals with Electric Charge, Electric Current, Electric Circuits and Electric Potential and Potential Difference, Ohms Law, Concepts of Resistance and Resistivity, Combination of Resistors, Heating Effect of current and Electric Power.
Full attempt is made to explain every concept so that it is very easy for the students and apply in appropriate situations (reasoning, solving numericals etc)
â€¢ Electric charge: this is the fundamental property of protons and electrons which gives rise to electric force between them.
â€¢ Electric current: the time rate of flow of charge through any cross section of a conductor is the measure of current
Electric current = total charge flowing/time taken
â€¢ Unit of electric current = ampere
â€¢ One ampere: the current through a wire is said to be one ampere if one coulomb of charge flows through it in one second.
â€¢ Direction of electric current is taken to be the direction of flow of positive charge or opposite to the direction of flow of negative charge (electron)
â€¢ Charge of an electron is = -1.6 x 10-19 C and charge of proton is : +1.6 x 10-19C (Q)
â€¢ Net charge on any body is given by
Q = Â± ne where
e = electric charge
n = number of charges
Qn: 1. Define one Ampere?
2. Calculate the number of electrons constituting one coulomb of charge?
we know, Q = Â±ne,
e= 1.6 x 10-19 C
n= 1/1.6 x 10-19 = 6.25 x 1018
â€¢ To set the electrons in motion in an electric circuit, we use a cell or battery. Current flows in a circuit from positive terminal to negative terminal of the cell.
â€¢ Current in the circuit is measured by an ammeter
â€¢ Define Electric Potential Difference
Electric potential difference between any two points in an electric circuit is the amount of work done (W) in moving a unit charge from one point to another.
â€¢ Potential difference V = work done (W) / charge (Q)
â€¢ Unit of potential difference = volt
â€¢ Define 1 Volt:
The potential difference between any two points in an electric circuit is said to be 1 volt if 1 joule of work is done in moving 1 coulomb of charge from one point to another.
â€¢ Potential Difference (p.d) is measured by a volt meter
â€¢ Ammeter is connected in series in the circuit and voltmeter is connected parallel across the points between which p.d is to be measured.
How much energy is given to each coulomb of charge passing through a 6V battery?
Ans: V= W/Q Therefore , W= VQ V=6V Q=1C
Therefore, W = 1J
â€¢ Ohmâ€™s law: The current through the conductor is directly proportional to the potential difference across the ends of the conductor provided the physical conditions such as temperature, pressure etc. are kept constant.
V ∝ I V = IR Where R= resistance of the conductor
â€¢ Resistance: It is the opposition offered by the conductor to the flow of charge trough it.
â€¢ Unit of resistance â€“ ohm (Ω).
â€¢ Define one ohm :
We know V=IR When V=1V, I=IA Then R=1Ω.
The resistance of a conductor is said to be one ohm if 1ampere of current flows through it when the p.d across it is 1volt.
â€¢ Factors on which the resistance of the conductor depends:
(i) R is directly proportional to the length of conductor (l).
(ii) R is inversely proportional to the area of cross section (A).
R ∝ l /A R =ρl / A.
When l= 1m A=1m2
Then R= ρ
Resistivity of the material of conductor is defined as the resistance of conductor of unit length and unit area of cross section
â€¢ Unit of Resistivity: Ωm.
â€¢ Both resistance and resisitivity of conductor depend on temperature (they increase with increase in temperature). It is because as the temperature is increased the electrons in the conductor undergo so much of collision with ions which increases the resistance.
â€¢ Resistivity depends on temperature, material of the conductor and not on the dimension of the conductor.
1. Compare the resistance of a conductor at 30oC and at 70oC
Ans: R70o>R30o (Resistance of the conductor increases with the increase in temperature)
2. A copper wire is stretched to twice its length. What happens to its resistivity?
Combination of resistances: when two or more resistances are connected in series the net or equivalent resistance is equal to the sum of individual resistances.
The total resistance in the above diagram is
R = R1+R2+R3 [derivation given in N.C.E.R.T]
â€¢ If R1>R2>R3 then R series>R1
â€¢ Equivalent resistance of series combination of â€˜nâ€™ equal resistances (each of value r) is given by Rs = nr
â€¢ Resistances in parallel :
â€¢ When two or more resistors are connected in parallel then the reciprocal of equivalent or net resistance is equal to the sum of the reciprocal of the individual resistances
1/Rparallel = 1/R1+1/R2 +1/R3
â€¢ If R1>R2>R3 then, Rparallel â€¢ Equivalent resistance of parallel combination of â€˜nâ€™ equal resistances (each of value r) is given by Rp = r/n
1) How many 176 resistances (in parallel) are required to carry 5A on a 220V line?
Resistance required in the circuit Rp = V/I = 220V/5V = 44 .
Resistance of each resistance r = 176 .
If â€˜nâ€™ resistors each of resistance â€˜râ€™ are connected in parallel then Rp = r/n i.e. is 44 = 176/n Therefore, 176/44 = 4
2) Which circuit has low resistance?
1. Three resistance R1, R2, R3 in series
2. Three resistances R1, R2, R3 in parallel?
Rparallel â€¢ Advantages of connecting electrical devices in parallel with the battery over connecting them in series.
ïƒ˜ When a number of electrical devices are connected in parallel, each device gets the same potential difference as provided by the battery and it keeps on working even if other devices fail to work, whereas in the case of devices connecting in series, when one device fails to work, all the other devices stop working.
ïƒ˜ Parallel circuit is helpful when each device has different resistances and requires different current for its operation as in this case the current divides itself through different devices. This is not so in series circuit where some current flows through all devices irrespective of their resistances.
HEATING EFFECT OF ELECTRIC CURRENT
â€¢ Whenever a current is passed through a conductor it becomes hot after sometime which means that electrical energy is converted to heat energy. This effect is called heating effect of electric current.
â€¢ Whenever a current I flows through a conductor resistance R for a time t, the amount of heat produced is given by heat H ï‚µ I2Rt
â€¢ The total work done by the source in maintaining the current in the circuit for a given time is called the electric energy consumed in the circuit.
W = VIt = I2Rt = V2t/R
â€¢ The rate at which work is done by the source (battery) in maintaining the current in the circuit is called the electric power of the circuit.
P = W/t = VI = I2R = V2/R
UNIT OF ELECTRIC POWER [WATT]
P = VI When V = 1 Volt and I = 1 Ampere, Then P = 1 Watt.
Definition of 1 Watt:
The power of an electric circuit is said to be one watt if one ampere of current flows through it when the potential difference across it is 1 Volt.
COMMERCIAL UNIT OF ELECTRIC ENERGY â€“ KWh
Definition of 1 KWh: It is the energy consumed when a an electrical device of power 1 KW works for one hour: 1 KWh = 3.6 x 106 J
1. What determines the rate at which energy is delivered by current?
2. An electric motor takes 5A from a 220V line. Determine the power of the motor and the energy consumed in 2h.
I = 5A, t = 2h = 7200 s.
Energy consumed W = VIt = 220 x 5 x 7200 = 792 x 104 J
Power P = VI = 220 x 5 = 1100 W
3. Why are Cu and Al wires usually employed for electrical transmission?
Copper and aluminium possess low resistivity and also cheaper than silver which has the least resistivity of all metals
4. Why does the cord of an electric heater not glow while the heating element does?
The cord of an electric heater is made of thick copper wire and has much lower resistance than its element. For the same current (I) flowing through the cord and the element, heat produced (I2 Rt) in the element is much more than that produced in the cord. Consequently, the element becomes very hot and glows whereas the cord does not become hot and as such does not glow.
Important formulae to remember
â€¢ Charge on a body
Q = ne Where n is number of charge carries & e electronic charge 1.6 x 10-19 C
â€¢ Current I = Q/t Q â€“ Charge T â€“ time
â€¢ Potentials difference V = W/Q Where W â€“ Work done Q â€“ Charge
â€¢ Ohms law V = IR
â€¢ V â€“ Potential different access the conductor
â€¢ I â€“ Current through the conductor
â€¢ R â€“ Resistance of conductor
R = ρl/A
Where ρ – Specific resistance of the material of wire
l â€“ Length of wire
A â€“ Area of cross section of wire
â€¢ Combination of resistances
â€¢ R Series = R1 + R2 + R3
â€¢ 1/Rparallel = 1/R1 + 1/R2 + 1/R3
â€¢ Electric energy supplied or electric work done is given by
â€¢ W = VIt = I2Rt = V2 t /R
â€¢ Electric power P = VI = I2R = V2/R
â€¢ Commercial unit of electrical energy 1 KWh = 3.6 x 106 J
Very short answer questions (1 mark)
1. Give the unit of (a) Charge (b) Current
2. Define current
3. Name the unit of (a) electrical resistance (b) resistivity
4. Define One Ohm
5. Define Resistivity
6. What is the resistance of a torch bulb rated at 2.5 V and 500 mA?
7. Two resistances of each 2 ohm are connected in parallel. Find their equalent resistance.
8. On what factors does the resistivity of a material depend?
9. Plot a graph between the Potential difference V and current I through a conductor
10. What happens to the resistance of the circuit if the current through it is doubled?
Short answer questions (2 marks)
1. Two wires of same material are having length L and 2L. Compare their resistance and resistivity.
2. Why are coils of electric toaster and electric iron made of an alloy rather then a pure metal?
3. Two wires are of same length and radius but one of them is copper and the other is of iron. Which will have more resistance? (Given the resistivity of copper = 1.62 x 10 -8 ohm meter and resistivity of iron = 10 x 10-8 ohm meter.
4. Define 1KWh. Give the relation between 1kwh and Joule.
5. State which has a higher resistance. A 50W or 25W lamp. Also find the ratio of their resistances.
6. A wire of resistance 5 Ohm is spent in the form of closed circle. What is the resistance between 2 points at the ends of any diameter of the circle?
7. Calculate the amount of charge that would flow in one hour through the element of an electric iron drawing a current of 0.4 amps.
8. A electric toaster of resistance 20 Ohm takes a current of 5A. Calculate the heat developed in 30 s.
9. A bulb is rated at 5V, 100mA. Calculate its (1) Power (2) Resistance
10. Name two special characteristics of a heater coil.
Short answer questions (3 marks)
1. Define resistance and resistivity. Give the relation between them. Explain the dependence of resistance on temperature.
2. With the help of neat circuit, derive the expression for the equalent resistance of 3 resistances connected in series.
3. With the help of neat circuit, derive the expression for the equivalent resistance of 3 resistances connected in parallel
4. (a ) Draw the circuit consisting of a battery of five 2V cells, 5ohm resistor, 10 ohm resistor, 15 ohm resistor and a plug key. All connected in series (b) Calculate the current passing through the above circuit when key is closed.
5. Two identical resistors each of resistance 2 Ohm are connected in turn (1) in series (2) in parallel to a battery of 12 V. Calculate the ratio of power consumed in two cases.
6. A piece of wire is redrawn by pulling it until its length is tripled. Compare the new resistance with the original value.
7. An electric kettle is rated 500W, 200V. IT is used to heat 400 gm of water for 30 secs. Assuming the voltage to be 220V calculate the rise in temperature of water. Specific heat capacity of water is 4200 J/Kg ÂºC.
8. In an experiment the current flowing through a resistor and potential difference across it are measured. The values are given below. Show that these values confirm Ohmâ€™s Law and also find the resistance of the resistor.
I (ampere) I(ampere) 1.0 1.0 2 1.5 2.0 2.0 2.5 2.5 3.0 3.0
V (volt) V(volt) 4.0 4.0 6.0 6.0 8.0 8.0 10.0 10.0 12.0 12.0
9. A heater draws 1100 W at 220V. (a) Find the resistance of the heater (b) Calculate the energy in KWh consumed in a week if the heater is used daily for 4 hours.
Long Answer questions (5 marks)
1. State Ohms law with a neat circuit. Explain how this law can be verified and also plot the expected v-I graph.
2. (a) Differentiate resistance and resistivity
(b) the ratio of resistivities of two materials a and b is 1:2, ratio of their length is 3:4 and if the ratio of radii is 2:3 find the ratio of resistance of a and b.