ohms law clearly states that
potential difference is directly proportional to the current flowing through the wire
or
V directly proportional to I ______(i)
so the formula which is derived is
$$V =IR \tag{1}$$
and now from this we can say that
$$I =\frac{V}{R}\tag{2}$$
So, from the equation 2
I(current) is inversely proportional to resistance ____________(ii)
now my question is ( from equation 1 ) :
if $I$ (current) is inversely proportional to resistance and directly proportional to the voltage then :
If the resistance is doubled then current will get halved
so, from (i) voltage will get halved …. but from equation 1 voltage is also directly proportional to resistance (because $V = IR$) then resistance should also get halved…. but previously we had doubled the resistance so this formula contradicts itself
in short….
when we doubled the resistance then current will get halved then voltage will also get halved and if voltage will get halved then resistance should also get halved.
So how to solve this contradiction?
Best Answer
Choose one to be held constant.
Suppose we supply the circuit with a constant power source, for example a $9$ $V$ battery.. If you double the resistance on the circuit, the current drawn from the power source will halved.
Suppose we changed out the $9$ $V$ battery with a $18$ $V$ power source while holding the resistance constant, the current will double.
There isn't a chain reaction like you think would happen. Everything happens in "one-step". Voltage will always reflect the current and resistance at that precise moment.
Just because I add more resistance, the loss in current isn't going to change my $9$ $V$ battery to a $4.5$ $V$ Battery.
The current is halved BECAUSE it's still a $9$ $V$ battery with doubled resistance.