CLASS X | SCIENCE | ELECTRICITY
notes prepared by subhankar Karmakar
Ohm's Law:
According to Ohm's Law, at constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.
If Ｉis the current flowing through a conductor and V is the potential difference (voltage) across its ends, then according to Ohm's Law:
Ｉ ∝ V (at constant temperature)
This can also be written as: V ∝ Ｉ
or V = RＩ
where R is a constant called "resistance" of the conductor. The value of this constant depends on the nature, length, area of cross section and temperature of the conductor.
V/Ｉ = R
The ratio of potential difference applied between the ends of a conductor and the current flowing through it is a constant quantity called resistance.
Therefore,
(i) The current is directly proportional to potential difference, and
(ii) The current is inversely proportional to resistance.
a. "Current is proportional to the potential difference" - it means if the potential difference across the ends of o conductor is doubled, the current flowing through it also gets doubled, and if the the potential difference is halved the current also gets halved.
b. "The current is inversely proportional to resistance" - it means if the resistance is doubled, the current gets halved, and if the resistance is halved the current gets doubled.
Resistance of a conductor:
The property of a conductor due to which it opposes the flow of current through it is called resistance.
The resistance of a conductor depends on length, thickness, nature of material and temperature of the conductor.
SI unit of resistance:
The SI unit of resistance is ohm. It is generated by the symbol Omega, Ω. The unit of resistance can be defined as following. "1 ohm is the resistance of a conductor such that when a potential difference of 1 volt is applied to its ends a current of 1 ampere flows through the conductor".
Numericals on Ohm's law:
1. Potential difference between two points of a wire carrying a 0.4 ampere current is 0.6 volt. Calculate the resistance between these points.
Soln: From Ohm's law we know that resistance of a conductor is equal to the ratio of the potential difference applied across the conductor and the current flowing through it. Therefore, R = V/Ｉ
or, resistance, R = 0.6/0.4 = 3/2 = 1.5 Ω
2. A simple electric circuit has a a 12 volt battery and a resistor of 60 ohms. What will be the current in the circuit? The resistance of the connecting wires is negligible.
Soln. From Ohm's law we know that current flowing through the circuit, Ｉ is equal to the ratio of the potential difference across the ends of the conductor V and the resistance R attached to it.
Therefore, Ｉ = V/R = 12/60 = 0.2 A (ampere).
3. An electric appliance draws a current of 2.2 ampere from a 220 volt supply line. What current will this electric iron draw when connected to 110 volt supply line?
Soln. From Ohm's law we know that resistance of a conductor is equal to the ratio of the potential difference applied across the conductor and the current flowing through it. As the resistance of the appliance is same.
R = V₁/Ｉ₁ = V₂/Ｉ₂
V₁ = 220 V, Ｉ₁ = 2.2 A, V₂= 110 V, Ｉ₂ = ?
Ｉ₂ = V₂Ｉ₁/V₁ = 110x2.2 /220 = 1.1 A
4. If 20 C of charge pass a point in a circuit in two second, what is the current flowing?
Soln. Charge passing through a conductor per unit time is called current. Therefore, current, Ｉ = q/t, q = charges passing through the conductor, t = time.
Ｉ = q/t = 20 /2 = 10 A
5. If a potential difference of 20 volt causes a current of 1 ampere to flow for 2 minute how much energy is transferred?
Soln. Q = Heat generated, Ｉ= Current = 1 A;
R = Resistance = V/Ｉ , t = time = 120 s
Q = Ｉ²Rt = ＩVt = 1 x 20 x 120 = 2400 Joules.
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