The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below: I (ampere) 0.5 1.0 2.0 3.0 4.0 V (volt) 1.6 3.4 6.7 10.2 13.2Plot a graph between V an I and calculate the resistance of the resistor?

Question

Answer

Plotting a graph between V and I

To plot a graph between V and I, we will take the values of I on the y-axis and the values of V on the x-axis. We will plot the given values of I and V as points on the graph and then join these points to get a straight line. This line is called the current-voltage (IV) characteristic of the resistor.

Calculating the resistance of the resistor

The resistance of the resistor can be calculated using the formula:

Resistance = Voltage / Current

We can use any of the given values of V and I to calculate the resistance. Let's use the first set of values:

Resistance = 1.6 / 0.5 = 3.2 ohms

We can calculate the resistance using any other set of values and we should get the same result.

Explanation

The graph we plotted is a straight line, which means that the resistor is a linear resistor. The slope of the line gives us the resistance of the resistor. We can see from the graph that as the voltage across the resistor increases, the current through the resistor also increases. This shows that the resistor is a ohmic resistor, which means that the current through the resistor is directly proportional to the voltage across the resistor.

Answer

V - I graph as shown in figure . Here points lie on the equation of line {where variables are V and I } are (1.6 ,0.5) , (3.4,1.0) , (6.7, 2.0) , (10.2, 3.0) and (13.2, 4.0)

Now , use Ohm's law ,

V = IR

R = V/I , means Resistance is the slope of graph V - I

So, R = (V₂ - V₁)/(I₂ - I₁)

V₂ = 3.4V, V₁ = 1.6V , I₂ = 1A and I₁ = 0.5A

So, R = (3.4 - 1.6)/(1 - 0.5) = 1.8/0.5 = 3.6

Hence, resistance , R = 3.6Ω

similarly R= (V₃ - V₂)/(I₃ - I₂) = (6.7 - 3.4)/(2 - 1) = 3.3

R = (V₄ - V₃)/(I₄ - I₃) = (10.2 -6.7)/(3-2) = 3.5

R=(V₅ - V₄)/(I₅ - I₄) = (13.2 - 10.2)/(4-3) = 3

here R is variable so, take average of all . Rav = (3.6 + 3.3 + 3.5 + 3)/4 = 13.4/4 = 3.35Ω

hence, resistance = 3.35Ω

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