When we have resistors in series, the current through all the resistors is same and the voltage drop (or simply voltage) at each resistor is different.
Question 1: It is fine that voltage drop (potential drop) across each resistor is different because each resistor offers different resistance (suppose). but how is the current through each resistor same? If we have resistors of different resistance, shouldn't the current be different through each resistor?
Similarly, when we have resistors in parallel, the current through each resistor is different but the voltage drop at each resistor is same.
Question 2: Current through each resistor is different because resistance of each resistor is different (suppose). but how is the voltage drop across each resistor same here? Shouldn't the voltage drop at each resistor be different because each resistor offers different resistance?
Answer
I'll start with current first...
1) "Current flows in a circuit" is the simple answer. In other words - It's the rate of flow of electric charges. Other than $i=\frac{dq}{dt}$, Current is also given by $I=nAEv_d$ which says something that it depends upon the drift velocity of electrons. The drift velocity is the average velocity between two successive collisions. This velocity prevents the electrons from accelerating continuously. Ok. Let's consider a circuit with three resistors with resistances in an increasing order $R_1>R_2>R_3$.
First, current enters $R_1$. After some collisions (causes heat generation), it exits the resistor. Now, the same current enters and exits $R_2$ & $R_3$ in the same manner. One point is to notice that, the rate of flow of charges is always the same (the current entered and exited the resistors with same magnitude). Only the drift velocities vary in different resistors.
If the same are connected in parallel (Now, we look into the resistors), current flows through $R_3$ easily. Because, $R_3$ requires a lesser $v_d$ (i.e) Electrons entering $R_3$ would exit within a small period of time relative to the other two (thereby increasing the rate)... As a result, larger current would be observed.
2) Voltage is simply the "Energy per unit charge" in both electrostatics & current electricity. Let's assume that the electrons have some energy and they pass through the series of resistors.
When the electrons encounter collisions within the resistor $R_1$, they lose their potential (which is referred to as "voltage drop") accordingly with their drift velocity (i.e) number of collisions which evolves as heat (depends upon the resistance of each). The remaining potential is still present in those electrons which drops across other resistors. Thus, the sum of each potential drop gives the total potential in that circuit.
As in case of parallel circuit, current has divided. Now, though the charges are taking different paths, they have the same potential (energy). Hence, the potential drop across each resistor would be the same... Man, It's all the consequence of Ohm's law $V=IR$.
Note: And, sorry for that confusion. Electrons gain energy only as they pass through the battery. But, they're always continuously accelerated by the electric field. Also, resistance is also given by $R=\frac{mL}{nAe^2\tau}$ which Simon Ohm replaced it as a constant (for a given temperature)...
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