Answer

Verified

386.1k+ views

**Hint:**To solve this question, we need to draw the circuit diagram according to the given information. Then using the Ohm’s law we can find out the expression for the current in the circuit in terms of the external resistance. From there we can predict the shape of the graph.

**Complete step-by-step solution**

According to the information given in the question, a cell of emf $ E $ and internal resistance $ r $ is connected across a variable external resistance $ R $ . So we can represent this information by the circuit diagram shown below.

The internal resistance and the external resistance are connected in series combination with each other. So the net resistance in the circuit is

$ {R_N} = R + r $.......................(1)

According to the question a current of $ I $ flows in the circuit. Therefore from the Ohm’s law we can write

$ E = I{R_N} $

From (1)

$ E = I\left( {R + r} \right) $

$ \Rightarrow I = \dfrac{E}{{R + r}} $ .......................(2)

This is the required equation of the current $ I $ in the form of the external resistance $ R $ .

Now, we substitute $ R = 0 $ in (2) to get

$ I\left( 0 \right) = \dfrac{E}{{0 + r}} $

$ \Rightarrow I\left( 0 \right) = \dfrac{E}{r} $

So the graph of this graph must pass through the y axis.

Now, we take the limit $ r \to \infty $ at both sides in (2) to get

$ \mathop {\lim }\limits_{R \to \infty } I = \mathop {\lim }\limits_{R \to \infty } \left( {\dfrac{E}{{R + r}}} \right) $

We know that $ \mathop {\lim }\limits_{x \to \infty } \left( {\dfrac{1}{{x + k}}} \right) = 0 $ . Therefore we have

$ \mathop {\lim }\limits_{R \to \infty } I = 0 $

So the graph must approach the x axis, as the value of the external resistance is increased infinitely. Hence, the graph of current $ I $ versus resistance $ R $ , is shown in the figure below.

**Note**

Do not try to obtain the plot by using transformations of the graph. Although we can obtain the plot by that method also, that would take much time and also chances of mistakes are huge. So after getting the equation, always guess the plot by substituting the end point values and taking the limits.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

The provincial president of the constituent assembly class 11 social science CBSE

Gersoppa waterfall is located in AGuyana BUganda C class 9 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The hundru falls is in A Chota Nagpur Plateau B Calcutta class 8 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE