Question

# Three cells of emf ( E, 2 E ) and ( 5 E ) having internal resistances ( r, 2 r ) and ( 3 r ) respectively are connected across a variable resistance ( R ) as shown in the figure. Find the expression for the current. Plot a graph for variation of current with ( R ).All India 2010 C

Solution

The current is ( I=frac{8 E}{6 r+R} )

Detail:

Given that,

Emf of first cell = E

Emf of second cell = ( 2 E )

Emf of third cell = ( 5 E )

Internal resistance of first cell = r

Internal resistance of second cell = ( 2 mathrm{r} )

Internal resistance of third cell = ( 3 r )

Variable resistance ( =mathrm{R} )

Now, the current

Current( =frac{text {total emf}}{text {Internalresistances}+text {variableresistance}} )

( I=frac{E+2 E+5 E}{r+2 r+3 r+R} )

( I=frac{8 E}{6 r+R} )

Hence, this is the required solution.