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Two cells of emfs 1.5 V and 2.0 V, having internal resistances 0.2 Ω and 0.3 Ω, respectively, are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.

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#### Solution

Given:

E_{1}=1.5^{ }V

E_{2}=2 V

r1=0.2 Ω

r2 =0.3 Ω

The effective emf of two cells connected in parallel can be calculated as follows:

`E_(eff) = (E_1r_2+E_2r_1)/(r_1+r_2)`

`=> E_(eff) = (1.5xx0.3+2.0xx0.2)/0.5 = 1.7 V`

The effective resistance can be calculated as follows:

`R_(eff)= (r_1r_2)/(r_1+r_2)`

`=> R_(eff)= (0.2xx.03)/0.5`= 0.12 Ω

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