Answer

Verified

346.2k+ views

**Hint:**First, the equivalent resistances have to be calculated for both series and parallel connections. Note that, there is no effect of lengths and diameters on the resistance since they are equal.

Next, the relationship between produced heat and resistance is to be used for two cases and find the ratio of produced heat.

**Formula used:**

Let the resistances for two conducting wires are ${R_1}$ and ${R_2}$.

So, equivalent resistance in series connection ${R_s} = {R_1} + {R_2}$

And, equivalent resistance in parallel connection ${R_p} = \dfrac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}$

The relation between produced heat $(H)$ and resistance $(R)$ is, \[H = \dfrac{{{V^2}t}}{R}\]

Where, $V$ is the potential difference and $t$ is the time.

**Complete step-by-step solution:**

Two conducting wires of the same material, same lengths and, same diameters are connected in two ways.

First in series and second parallel connection.

Let the resistances for two conducting wires are ${R_1}$ and ${R_2}$.

Since, the material, lengths and diameters are the same the resistances are equal. Hence, ${R_1} = {R_2} = R$

So, equivalent resistance in series connection ${R_s} = {R_1} + {R_2} = 2R$

And, equivalent resistance in parallel connection ${R_p} = \dfrac{{{R_1}{R_2}}}{{{R_1} + {R_2}}} = \dfrac{{{R^2}}}{{2R}} = \dfrac{R}{2}$

The relation between produced heat $(H)$ and resistance $(R)$ is, \[H = \dfrac{{{V^2}t}}{R}\]

Where, $V$ is the potential difference and $t$ is the time.

So, $H \propto \dfrac{1}{R}$

$\therefore \dfrac{{{H_s}}}{{{H_p}}} = \dfrac{{{R_p}}}{{{R_s}}}$ where, ${H_s}$ and ${H_p}$ heat produced in series and parallel combinations respectively.

$ \Rightarrow \dfrac{{{H_s}}}{{{H_p}}} = \dfrac{{R/2}}{{2R}}$

$ \Rightarrow \dfrac{{{H_s}}}{{{H_p}}} = \dfrac{1}{4}$

So the ratio of ${H_s}$ and ${H_p}$ is $1:4$ .

Hence, the right Option is $C) \Rightarrow 1:4$

**Note:**For a conductor of length $l$, area $A$ and, electric conductance $\rho $, the resistance $R = \rho \dfrac{l}{A}$

Hence for two conductors of the same material, same lengths and, same diameters, the resistances will be the same.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

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

How many crores make 10 million class 7 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE