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Why does same current $I$ flow in the series circuit but it isn't the case with resistors in parallels?

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Perhaps you meant intuitively? Well, if you imagine the roads are tracks and the flow of cars the current, and if you had the choice between a very bumpy narrow path on your left and a very nice motorway on your right, which would you choose? Everyone will start to go right, and as the right path gets more and more crowded, some will start to go left, until equilibrium is reached. The flow of cars to the right will then be inversely proportional to the relative quality of the road on the left, and therefore the overall flow of cars on the right will be higher. In this analogy, the quality of the road is the resistance. On the other hand, if you had a motorway ending on a footpath (i.e. series arranement, as opposed to parallel), no matter how fast you can go on a motorway its flow of cars will be the same as the one that clears the footpath.

That's the simplistic version which you can also illustrate more classically with water in pipes.

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Probably the best way to explain this is using water pipe analogies. In a series, the water only haas one pipe. To flow through, thus all current(water) flows through the pipe. In a parallel circuit however, there is a T junction for the water to flow through. Now if the pipes attached to the T junction are two different sizes, more water will naturally flow throuhg the larger pipe. In the case of a circuit, the larger pipe is the resistor with a lower resistance. Hence the difference in current flow through resistors in parallel.

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Kirchhoff's first law says: "At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node". When there is only one current flowing into the node it is simply equal to the sum of currents flowing out. The node or junction is the place where conductor splits to form couple parallel branches.

When You have resistors in series, there is no such node/junction, the current doesn't split and flows through each resistor.

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In series circuits, resistances add can be simply added and treated as one big effective resistance: $R_{\text{eff}}=R_1+R_2+R_3$.... So the current remains same. In parallel circuits the current splits up so each branch has a different effective resistance (in each of the separate branches one can use the series rule again). Due to this, the current isn't the same everywhere in a parallel circuit.

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Most basic concepts that must be understood here are "Voltage" and "Current" .

  1. Voltage: Voltage is difference in electric potential between two points/nodes.
  2. Current: Current is simply flow of electric charge and is defined by Ohm's Law as: $$I =\frac {V}{R}$$

Now, in a series circuit, all resistors are placed between two nodes. Voltage among these two nodes is kept same. Total resistance between two nodes is simple addition of individual resistances. So, In a series circuit, voltage and resistance both remain constant and hence same current I, ( which equals $I =\frac {V}{R}$) flows though the circuit.

While in parallel circuit, resistances are not placed one after one and are connected separately in separate branches between two nodes. So voltage between two nodes remains same but current has now different branches to flow from node one to node two. So current distributes itself according to the values of resistances in branches. And hence in parallel circuit, same current doesn't flow, in fact cannot flow, from node one to node two.

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but it isn't the case with resistors in parallels

(1) parallel connected resistors have identical voltage across

$$V_{R1}=V_{R2}$$

(2) the voltage across a resistor is given by Ohm's law $V_R = I_R\cdot R$. Applying Ohm's law to parallel connected resistors yields

$$I_{R1}\cdot R_1 = I_{R2}\cdot R_2$$

Thus, conclude that the parallel connected resistor currents can only be equal if the resistances are equal.

Why does same current I flow in the series circuit

Actually, this defines series connected circuit elements - two resistors are series connected if and only if the resistor currents are identical (not simply equal).

In other words, if all of the current leaving one terminal of a resistor enters one terminal of another resistor, the two resistors are series connected.

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protected by Qmechanic Mar 12 '16 at 1:39

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