Question

Two cells of emf 1.5 Volt and 2 Volt
having respective internal resistances of 1
22 and 2 s2 are connected in parallel so as
to send current in same direction through
an external resistance of 5 12. Find the
current through the external resistance.
[Ans: 5/17 A]​

Answer 1

Answer:

EMF E_{1}=1.5 voltE

1

=1.5volt

EMFE_{2}=2.0 voltE

2

=2.0volt

Internal resistance r_{1} = 0.2r

1

=0.2

Internal resistance r_{2} = 0.3r

2

=0.3

Effective emf of two cells connected in parallel is,

E_{eff}=\dfrac{E_{1}r_{2}-E_{2}r_{1}}{r_{1}+r_{2}}E

eff

=

r

1

+r

2

E

1

r

2

−E

2

r

1

E_{eff}=\dfrac{1.5\times 0.3+2.0\times0.2}{0.2+0.3}E

eff

=

0.2+0.3

1.5×0.3+2.0×0.2

E_{eff}=1.7\ VE

eff

=1.7 V

Now, the effective resistance of equivalent cell is

R_{eff}=\dfrac{r_{1}r_{2}}{r_{1}+r_{2}}R

eff

=

r

1

+r

2

r

1

r

2

R_{eff}=\dfrac{0.2\times 0.3}{0.2+0.3}R

eff

=

0.2+0.3

0.2×0.3

R_{eff}=0.12\OmegaR

eff

=0.12Ω

Hence, The emf and internal resistance of the equivalent cell are 1.7 V and 0.12 ohms.