Prove mathematically as well as theoritically that voltage remains same in parallel whereas got divided in series connection
Answers
Explanation:
This kind of misconception can be cleared by the definition itself.
Voltage is the energy per free electron (which contributes to current flow in the conductor), whereas current is the rate of flow of free electrons across the conductor's cross-sectional area. In other words, current is the count of the stuff that passes through the cross-section within a given time period and voltage is what drives the stuff.
Charge is a conserved quantity. What you perceive as heat is the energy of the particles1 flowing at the drift speed (around a few millimeters per second). It's simply the voltage that's converted to heat. The free electrons can't smell around and divide accordingly based on resistance on each path of the circuit. It's just a random flow. They just go around and when the path-division is encountered, some go through one way and some go through the other.
Circuit
To dig further inside, let's consider a parallel network like the one here (ABCDEFA). The battery (DC) maintains a potential difference (how much doesn't matter for now) which is far enough for the charges2 to start flowing. These charges encounter a junction B on the way. As previously told, there's no specific condition that reroutes the charges to some preferred direction. It's simply random. Hence, some follow the path BE, while the remaining go via CD to reach the battery.
Say the resistance of R2>R1. What would happen? The time taken by the charges to swim through R2 is greater than it takes through R1. So, a lot of charges can get out of R1 within a specific time period, while the number is less in case of R2. And, this happens within a few seconds once the potential difference is established and that's why we perceive that the current through R2 is less than the one through R1 (which is the reason why "current divides in parallel circuits).
Once the charges get out of the resistors, the electric field of the battery is enough to drive them mad (as the wire has relatively lower resistance). And, the charges get back their energy once again. This is the reason why we say voltage is the same in parallel circuits3.