Question

draw a graph to Verify Ohm's law for two wires A and B such that a has greater resistance than B​

Answer 1

Answer:

Explanation:

We need to find which conductor A or B has greater resistance.

We know what resistance is it is basically the ratio of the voltage and the current. The higher the voltage and lesser the current more is the resistance applied.

For finding the greatness in the resistance of a conductor of the above graph we only need to compare the ratios of the above conductors’ voltage and current.

For doing so firstly we need to do some thinking or assumptions.

Let us take the voltage of the A and B conductors be V and v.

And let us take their respective currents be I and i.

We need to observe the graph right now. For observation in graph we will find what actually the voltage of current of both conductors in the graph and what is the relationships between the voltages of both the conductors. We also need to find relationship between the current of both conductors. For finding the voltages and current we firstly redraw the diagram .

Now we draw the separate diagrams for A and B

Construction:

we have perpendicular AM and AN on voltage and current axis respectively drawn.What we have formed is a rectangle. Which means

ON=AM and OM = AN

Now we know that AN=the voltage and AM= current for the conductor A.So the voltage value must be equal to OM on voltage axis and current value equals to ON on current axis. OM= voltage and ON =current.

Construction:We have drawn perpendicular BQ and BP on voltage and current axis respectively. What we have formed is a rectangle which means BQ=PO and BP=OQ. Now we know that BP is the voltage and BQ is the current as they are parallel to their respective axis which means the line parallel to the voltage axis is the voltage value for B. Now we need to compare the values within the axis . so OQ is the voltage value on voltage axis as it is equal to BP and PO is the current value on current axis . OQ=voltage value and OP = current value

Comparing the current values for A and B conductors

From the above diagrams we can see that ON is less than OP. It can be explained very well if we merge the diagrams together and then notice.

So , ON< OP

ON = current value of A= I{from line6}

OP=current value of B=i{from line6}

So we can write it as that I<i giving this name equation(1)

Comparing the voltage values for A and B conductors

From the above diagrams we can see that OM is greater than OQ.

So, OM>OQ

OM=voltage value for A = V

OQ= voltage value of B=v {from line5}

So we can write it as V>v

For the sake of convenience we write it as v<V giving this name equation(2)

We write it only because we wanted LHS and RHS of the equation first and second to have same signs.

So in the next few lines we are going to prove which is of greater resistance A or B.

Let’s multiply equation(1) and equation(2)

We get, I*v<i*V

Dividing the whole equation by I*i . i just did it to make it simple you can just cross multiply both currents and do not change voltages.

Now we get v/i<V/I

We know that by ohm’s rule that voltage/current equals resistance. So for v/i the resistance is small r or resistance of conductor B as small v and small i are both the components of B , similarly the V/I equals R or resistance of A.

Now we rewrite the equations after putting values:

r<R

r= Conductor B resistance and R= resistance of conductor A

so

resistance of B<resistance of A

this is a long description to fully describe you how it happens but if you wanted to quickly know which resistance is greater compare the voltages and currents by seeing diagram then think in the way described below:

if the voltage of A is greater and its current is less as in comparison to B it gives out a greater value of resistance.

Why? Simply because in ratios voltage is the numerator and current is denominator . voltage of A is greater means numerator is greater and also denominator is less. So there is a big value of A’s resistance . take for example of two ratios:

First one being 5:2 and second 4:3

So 5 is greater than 4 and 2 is less than 3. So 5:2 equals 2.5

And in the second ratio 4:3 which equals 1.33

So the first has a higher value than second. And we get the required result.

Now there is a more simple method I can say

We know the graph is between I and V and the slope of the graph i.e. I/V gives 1/R

AND I/V is tanx where X is the angle made by the line with positive X direction

So by this the greater the angle the lesser the resistance as tanx=1/R.

Hope the answer helps