Question

two cells each of EMF 1.5 volt are joined in series and send 1.8 ampere current in an external resistor if the same cells are joined in parallel then they send 0.6 ampere current in the same resistor what is the internal resistance of each cell​

Answer 1

Given that,

EMF = 1.5 V

Two cells are joined in series then,

Current = 1.8 A

Two cells are joined in parallel then,

Current = 0.6 A

Let internal resistance be r and external resistance be R

In series combination,  

$Net\ emf = 1.5+1.5$

$Net\ emf = 3 \ V$

Net resistance = R+2r

We need to calculate the internal resistance

Using formula of resistance

In series combination,

$E=i(R+2r)$

Put the value into the formula

$3=1.8(R+2r)$

$3=1.8R+3.6r$.....(I)

In parallel combination,

EMF = 1.5 V

$E=i(R+\dfrac{r}{2})$

Put the value into the formula

$1.5=0.6(R+\dfrac{r}{2})$

$5=2R+r$

Now, multiply by 2 of equation (I)

$6=3.6R+7.2r$

Now, multiply by 1.8 of equation (II)

$10=3.6R+1.8r$

From equation (I) and (II)

$-4=5.4r$

$r=-\dfrac{4}{5.4}$

$r=0.7$

Hence, The internal resistance is 0.7 ohm.