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Two cells of emfs 1.5 V and 2.0v hav...

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

Text Solution

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`E_1 = 1.5 V, r2 = 0.2Omega`
`E_2 = 2.0 V, r_2 =0.3Omega`
emf of equivalent cell’
`E=(E_1/r_1+E_2/r_2)/(1/r_1+1/r_2)=(E_1r_2+E_2r_1)/(r_1+r_2)`
`=((1.5xx0.3+2xx0.2)/(0.2+0.3))=(0.45+0.40)/(0.5)V=1.7V`
Internal resistance of equivalent cell
`1/r=1/r_1+1/r_2=(r_1r_2)/(r_1+r_2)`
`=((0.2xx0.3)/(0.2xx0.3))Omega=(0.06)/(0.5)Omega=0.12Omega`
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