Why in a circuit with resistors in -
• parallel has potential difference constant in whole circuit but not current.
• series has current constant in whole circuit but not potential difference.
It states that V=iR only when the physical conditions around the conductor remains constant.
So if i have many resistors connected in parallel and then the voltage will be same. Actually, resistance is the property which basically opposes the flow of current. The higher the resistance of a conductor the less will be the current flowing through it. So if i have different valued resistors connected in parallel then the currents flowing through them will adjust in such a way that the product of R and i remains the same i.e Voltage remains constant. The flow of current across any branch is dependent on the value of resistance of that branch of the network. If the resistance is high then the current will be low and vice versa. This high low trade off between resistance and current is done only by keeping their product constant i.e V= constant in parallel.
If we talk about series connection then current will be same. It can very easily be understood by considering a small example which just striked my mind. Suppose we have 10 persons standing in a queue. And now if i give a ball to first person and ask him to pass the ball to his immediate neighbour and the same procedure is done by the neighbour then at the 10th person, i will receive the same ball without any changes in shape, size, etc. Similar is the case with current. Current is that ball and those 10 persons are the network elements connected in series. In series current doesn’t divide but the same current flows through all the devices connected in series. Each device use the incoming current for their operation and pass the same current ahead to the next device. Well ofcourse, this is the ideal case that i am talking about.