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Ohm's Law

Ohm's Law states that the current flowing through a device is directly proportional to the potential difference applied to the device. The constant of proportion is called the resistance of the device when it is formulated mathematically as:

V = I R
Where V is the voltage across an element of the circuit in volts, I is the current passing through the element in amps and R is the resistance of the element in ohms. Given any two of these quantities Ohm’s law can be used to solve for the third.

Corresponding SI units:
volt (V) = ohm (Ω) ∙ ampere (A)

Ohm's Law can be rewritten as:
I = V/R
R = V/I


Electrical circuit for Verification of Ohm's Law:
To verify Ohm's law, the following circuit is used. 


The above diagram is of the circuit used in the lab for verification of ohm's law.
In the circuit: B is the battery to supply the current to the circuit, Rh is rheostat to control the current in the circuit, K is key to connect or break the circuit, A is ammeter to measure the current in the circuit, V is the voltmeter to measure the potential difference across the resistance wire and R is a resistance wire to provide resistance.

Points to note:
1. The Rheostat Rh, the key K, ammeter A, and the resistance wire R are connected in series with the battery B.
2. The positive side of the ammeter should be towards the positive terminal of the battery.
3. The voltmeter V is connected parallel to the resistance wire.
4. The positive side of the voltmeter should be towards the positive side of the battery.


Procedure for the Verification of Ohm's Law:
1. Key K is closed and the Rheostat is adjusted so as to get minimum reading in the ammeter and voltmeter.
  1. The rheostat is then gradually moved so that the current in the circuit increases.
  2. Each time the rheostat is moved, the readings of the current (I) flowing in the circuit and potential difference across the resistance is measured by noting the readings of the ammeter and voltmeter.
  3. Thus, different sets of values are obtained in a table and the ratio of the current (I) and the potential difference (V) is calculated for each set of values.
  4. It is noted that the ratio of the current and potential difference is same or almost the same for each set of values in the table.
  5. Now a graph is plotted for V against I, in which the potential difference V is taken on the y axis and the current I is taken on the x axis.
  6. The graph obtained is a straight line and the slope of this line is the value of the ratio of V verses I.


Thus it is proved that the ratio of V verses I is a constant value (denoting resistance), that is, V/I = constant = R. Thus Ohm's law is verified.


Example 1: A current of 5mA flows through an Ohmic conductor which has a potential difference of 15V applied across it. What is the resistance of the conductor?
Solution:
Using V = I R
Transposing, R = V/I
where I = 5mA and V = 15V

gives R = 15/5=3kΩ


Example 2: What current will flow through a resistor whose resistance is 4.7k when a voltage of 12V is applied across it?
Solution:
Using V = I R
Transposing, I = V/R
where V = 12V and R = 4.7k

gives I =12/4.7= 2.55mA


Example 3: What is the voltage across a conductor whose resistance is 10Ω when a current of 500mA flows through it?
Solution:
Using V = I R
where I = 500mA and R = 10Ω

gives V = 500 × 10-3 × 10 = 5V


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