Question

a)Two cells of emf E1 and E2 have their internal resistance r1 and r2 respectively. Deduce an expression for the equivalent emf and internal resistance of their parallel combination when connected across an external resistance R. Assume that the two cells are supporting each other. (b) In Case the cells are identical, each of emf = 5V and internal resistance r = 2 Ω, calculate the voltage aross the external resistance R = 10 Ω.​

Answer 1

Answer:

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Explanation:

10 ()56(7)-& traditional

Answer 2

The equivalent emf :

Explanation:

Let emf of cell is ε1 & ε2.

Let the internal resistance are r1 & r2.  

Let V is the potential difference between B1 and B2.

$\displaystyle I=\frac{\varepsilon _{1}-V}{r_{1}}+ \frac{\varepsilon _{2}-V}{r_{2}}$

$\displaystyle I=\left ( \frac{\varepsilon _{1}}{r_{1}}+\frac{\varepsilon _{2} }{r_{2}} \right )-V\left ( \frac{1}{r_{1}}+\frac{1}{r_{2}} \right )$

$\displaystyle V = \left ( \frac{\varepsilon _{1}r_{2}+\varepsilon _{2}r_{1}}{r_{1}+r_{2}} \right )- I\left ( \frac{r_{1}r_{2}}{r_{1}+r_{2}} \right )$

If we replace this with a single cell it can be defined as

$\displaystyle V = \varepsilon _{equivalent}-Ir_{eqivalent}$

$\displaystyle \varepsilon _{eqivalent} = \left ( \frac{\varepsilon _{1}r_{2}+\varepsilon _{2}r_{1}}{r_{1}+r_{2}} \right )$

$\displaystyle \mathbf{ r_{equivalent} =\left ( \frac{r_{1}r_{2}}{r_{1}+r_{2}} \right )}$

b)

Given:

E = 5V

r = 2 Ω

R = 10 Ω

To find:

V =?

Step to step explanation:

The effective resistance in terms of resistance is given by

$\displaystyle \\r_{eff}=\frac{r}{2}$

       =  $\displaystyle \frac{2}{2}$

     r = 1 Ω

Now, the emf across the resistance is given by

E = IR

$\displaystyle I = \frac{E_{eff}}{R + r}$

 I =  $\displaystyle \frac{5}{11} A$

We know that,

V = IR

$\displaystyle V = \frac{5}{11} \times 10$

V = 4.54 V