in physics,resultant resistance in series is greater than resultant resistance in parallel.why?

Answer 1

Let's use Ohm's law: V=IR. I=current, R=resistance, V=Voltage.

For a pair of resistors in series, the same amount of current flows through both resistors. The voltage drop varies across each resistor, but the total drop is the same, so:

Total V= I * Total R ,
V1 = I * R1
V2 = I * R2, and
Total V=V1+V2

mixing these equations:
V1+V2=I * Total R
I*R1 + I*R2 = I*Total R

I cancels out, so for series, total R = R1+R2. The resultant resistance is larger than either resistance.

For parallel circuits, again using 2 resistors, the VOLTAGE is the same for both resistors. Current through each resistor may me different, but the total current is maintained. In equations:

Total V=V1=V2 = V
I1+I2 = Total I

from Ohm's law, V=IR, we can get:

I=V/R , so:

Total I = I1 + I2
Total V / Total R = V1/R1 + V2/R2, or
V/Total R = V/R1 + V/R2

V cancels out. so we are left with:

1/Total R = 1/R1 + 1/R2

for parallel resistors. The resultant resistance is always smaller than the individul resistances.

If we compare the resultant resistances of both connections, we can easily see that the resistance of the series circuit is always greater than the same resistors in parallel.

Answer 2

As for parallel, it's easy: More cars per hour can flow from city A to city B if they are connected by a four-lane freeway than by a two-lane freeway.

As for serial, it's less intuitive, since the number of cars that can flow between the two cities does not depend on the distance between them. But it has to do with the way voltage and resistance are defined. If the voltage between A and B is 110 V, it means that each Coulomb (1.6*10^19 electrons) has 110 Joule more energy in A than in B. Think of city A being 110 meters higher in the hills than city B.

Now if the length of the wire ("distance") doubles while the Voltage ("height") remians the same, the elctrical field strength ("steepness") decreases, so the electrons ("cars") flow slower.

Answer 3

Resistance in series gives the current only one path and the resistance adds. But resistance ion parallel gives the current two paths, thus giving less resistance.

Consider a voltage source V that produces current I. V = IR Ohm's law and Kirchoff's voltage law states that the voltage drops in a loop equal the voltage gains in a loop. If you have your resistance in series, there is only one loop. Therefore V = I(R1+R2). If you place the resistors in parallel, there are two loops. For loop 1, V = I1R1 and for loop 2 V = I2R2. Let I = I1+I2, and w see from before that I1R1 = I2R2. Therefore I2 = I1(R1/R2). Therefore I = I1+I1(R1/R2) = I1(1+R1/R2) = I1(R2+R1)/R2. Putting this in equation V=I1R1, we get V=I(R1R2/(R1+R2)). This equivalent resistance is always less than R1 or R2 alone.

By the way (R1R2/(R1+R2)) = 1/(1/R1 + 1/R2), not 1/R1 + 1/R2 like the guys above say.

Answer 4

2 ways to think.......

1st : Maths

for series.......u add no.s which is greater than the formula for parallel

2nd : Logic

resistance is offered by particles/atoms of the substance. If you provide and alternate path ( as in the case of parallel ), you have more chances of current passing through but in case of series, an added hurdle awaits after passing each resistor.

Answer 5

in series resistance is greater,it can be proved
resultant resistance=r1+r2+...
parallel circuit
1/r1+1/r2
so by calculation u can prove that resulatant resistance in series is greater than in parallel.i have told you mathematically but cannot tell u theoretically.sorry
take care

Answer 6

the comprehensive resistance of a series circuit will boost as greater plenty are related in series and is the sum of each and every of the guy load resistances *AND* the resistance of the twine connecting them.

Answer 7

my answer agrees with dude , but in simple , from the fact that for series connection the current is same I1=I2=I3=I ,the total voltage V= IR= V1+V2+V3=I(R1+R2+R3) So that total resistance R=R1+R2+R3. for parallel connection the voltage is the same V1=V2=V3 , the total current =V/R= I1+I2+I3=V(1/R1 +1/R2 +1/R3 ) So that 1/R= 1/R1 +1/R2 +1/R3

Answer 8

In electric circuits in series the electricity goes through all the resistors.
In parallel circuits, the electricity only goes through one or the other, there is less current through each one.

Answer 9

because when resistors are placed in paralell the current divides itself hence when there is less current obvioulsy the lower the resistance

Answer 10

in series r =r1+r2 etc; in parallel its 1/r1 + 1/r2 etc.