A battery of e.m.f. 10 V and internal resistance 4 ohm is connected to a parallel combination of two resistors of resistances 10 ohm and 15 ohm. Calculate the terminal voltage of the battery.

Explanation

E = 10 V
`r = 4Omega`
`R_(1) = 10Omega, R_(2)= 15 Omega, V =?`
`:. R_1 and R_2` are in parallel and let their net resistance be R.
`1/R =1/R_(1) + 1/R_2`
`implies1/R=1/10+1/15=(3+2)/30 =5/30=1/6`
`implies R = 6Omega`
Now `r=(E/V-1)R`
`implies 4 = (10/V-1)6`
`implies10/V-1=4/6=2/3`
`implies 10/V =2/3 +1 =5/3`
`implies V = (10 xx3)/(5) = 6` volt