ELECTRICITY

Concepts to be covered:

Electric current and Circuit , Electric Potential And Potential Difference , Circuit Diagram , Ohm’s law , Factors on Which the Resistance of a conductor depends , Resistance of a system of Resistors , Heating effect of Electric Current , Electric Power.
MCQs,1mark, 2 mark , 4 mark questions.

Electric current And Circuit

Electric current is defined as the amount of charge flowing through a particular area in unit time. Electrons were not known at the time when the phenomenon of electricity was first observed . The direction of flow of positive charges was taken to be the direction of electric current. In an electric circuit the direction of electric current is taken as opposite to the direction of the flow of electrons, which are negative charges.

If a net charge Q, flows across any cross section of a conductor[the material which transfers energy from battery (source) to the bulb] in time T, then the current I, through the cross-section is I=Q/T.

The SI unit of electric charge is Coulomb(C), which is equal to 6 * 10^18 electrons.[the electron possesses a negative charge of 1.6 * 10^-19 C]. The electric current is expressed by a unit called AMPHERE(A). The circuit consists of battery, key , bulb, copper wire, ammeter[it measures the electric current in a circuit.]

EXAMPLE 1:

A C current of 0.5A is drawn by a filament of an electric bulb for 10 minutes. Find the amount of electric charge that flows through the circuit.

SOLUTION: we are given, I=0.5A ; T=10 min = 10*60s =600s we have Q=IT =0.5 A * 600 s =300 C

Electric potential And Potential Difference:-

For the flow of electric charges in a conducting metallic wire; the electrons move only if there is a difference of electric pressure-called potential difference.

EXAMPLE 2: How much work is done in moving a charge of 2 C across two points having a potential difference 12V ?

SOLUTION : we know that, W=VQ

=12 V * 2 C =24 J

We define the electric potential difference between two points in an electric circuit carrying some current as the work done to move a unit charge from one point to the other-

potential difference(V) between two points =Work done(W) / Charge(Q)

The S.I unit of electric potential difference is volt(V). 1 volt =1 joule / 1 coulomb. The potential difference is measured by means of an instrument called the Voltmeter. The voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

Circuit Diagram :-

OHM’S LAW:

set up a circuit as shown in figure
First use only one cell as the source in the circuit. Note the readings in ammeter I ,for the current and reading of the voltmeter V for the potential difference across the wire XY in the circuit . Note the readings in the given table .
Next connect the two cells in the circuit and the readings of the ammeter and voltmeter.
Repeat the above steps using three cells and then four cells in the circuit separately .

Calculate the ratio of V to I for each pair of potential difference and current.

plot a graph between V and I ,and observe in the nature of the graph in shown in above figure.

We observe that V-I graph is the straight line passes through the origin of the graph. Thus, V/I is a constant ratio . The potential difference V, across the ends of a wire in the circuit is directly proportional to the current flowing through it , provides its temperature remains the same. This is called Ohm’s law.

V/I = constant = R

V=IR, where R is called the resistance . It is the property of a conductor to resist the flow of charges through it. Its SI unit is ohm . It is represented by Ω.

According to the ohm’s law ,

I=V/R , the current through the resistor is inversely proportional to its resistance. If the resistance is doubled the current gets halved.

RESISTANCE: a component used to regulate the current without changing the voltage source is called the resistance.

RHEOSTAT: it is often used to change the resistance in the circuit.

A component of a given size that offers low resistance is called the good conductor. A component having some appreciable resistance is called the RESISTOR.

FACTORS ON WHICH THE RESISTANCE OF A CONDUCTOR DEPENDS

The resistance of the conductor depends on is length , on its area of cross section and on the nature of the material . The resistance of a uniform metallic conductor is directly proportional to its length(l) and inversely proportional to the area of the cross-section(A).

R = ρ( l/ A)

where ρ(rho) is a constant called ELECTRIC RESISTIVITY of the material of the conductor. The SI unit of resistivity is Ω m.

The metals and alloys have very low resistivity in the range of 10^-⁸Ω m to 10^-6 Ω m. They are good conductors of electricity. Insulators like rubber and glass have resistivity in

the order of 10¹² to 10¹⁷ Ω m.

EXAMPLE 3:

(a) How much current will an electric bulb draw from a 220 V source, if the resistance of the bulb filament is 1200 Ω?

(b)How much current will an electric heater coil draw from a 220 V source, if the resistance of the heater coil is 100 Ω ?

SOLUTION :

(a)given, V=220 V ; R = 1200 Ω

From the ohm’s law, I =V / R (I = 220 V / 1200 Ω =0.18 A)

(b) we are given , V = 220 V ,R=100Ω

I= 220 V / 100 Ω = 2.2 A

EXAMPLE 4: Resistance of a metal wire of length 1m is 26Ω at 20°C . if the diameter of wire is 0.3 mm, What will be the resistivity of metal at that temperature? Predict the material of the wire .

SOLUTION: given, the resistance R , =26 Ω , the diameter d = 0.3 mm = 3*10^-4 m , and the length l of the wire =1 m .

the resistivity of the wire is , ρ =(RA/ l) =( Rπd² / 4 l )

ρ = 1.84 * 10^-6 Ω m.

The resistivity of the metal at 20°C is 1.84 * 10 ^-6Ω m. This is the resistivity of the manganese.