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derivation of resistors in series and in parallel ?

When the resistors are connected in series combination then the

equivalent resistance is Rs = R1 + R2 + R3

When the resistances are connected in the parallel combination

then the equivalent resistance is

  (1 / Rp) = (1 / R1) + (1 / R2) + (1 / R3)

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for series--

take 3 resistors R1, R2 and R3 connected in series and a battery of V volts has been connected. suppose the p.d across R1 is V1, R2 is V2 and R3 is V3.

total p.d across the 3 resistors should be equal to the voltage of the battery i.e.

V = V1 + V2 + V3 __________[1]

from ohm 's law--

V = IR ___________[2]

V1 = IR1 _________[3]

V2 = IR2 _________[4]

V3 = IR3 _________[5]

putting values of V1, V2 and V3 in [1]

IR = IR1 + IR2 + IR3

=IR = I [R1 + R2 + R3]

=R = R1 + R2 +R3

for parellel--

take 3 resistors R1, R2, R3 connected in parellel and connect a batery of V volts. in this case the p.d across the ends will be the same. the current flowing, however, is not the same.

total I = I1 + I2 + I3 _______[1]

from ohm 's law--

I = V / R _______[2]

I1 = V / R1 _________[3]

I2 = V / R2 __________[4]

I3 = V / R3 _________[5]

putting the values of I1, I2 and I3 in [1]

V / R = V / R1 + V / R2 + V / R3

= V / R = V [1 / R1 + 1 / R2 + 1 / R3]

= 1 / R = 1 / R1 + 1 / R2 +1 / R3

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Since, sum of voltage drops across the individual resistance is nothing but the equal to applied voltage across the combination.

Now, if we consider the total combination of resistances as a single resistor of electric resistance value R, then according to Ohm’s law,

V=IR --(2)

Now, comparing equation (1) and (2), we get

So, the above proof shows that equivalent resistance of a combination of resistances in series is equal to the sum of individual resistance. If there were n number of resistances instead of three resistances, the equivalent resistance will be

Resistances in Parallel

Let’s three resistors of resistance value R1, R2 and R3 are connected in such a manner, that right side terminal of each resistor are connected together as shown in the figure below, and also left side terminal of each resistor are also connected together. parallel-resistor This combination is called resistances in parallel. If electric potential difference is applied across this combination, then it will draw a current I (say). As this current will get three parallel paths through these three electrical resistances, the current will be divided into three parts. Say currents I1, I1 and I1 pass through resistor R1, R2 and R3 respectively. Where total source current Now, as from the figure it is clear that, each of the resistances in parallel, is connected across the same voltage source, the voltage drops across each resistor is same, and it is same as supply voltage V (say). Hence, according to Ohm’s law, Now, if we consider the equivalent resistance of the combination is R. Then, Now putting the values of I, I1, I2 and I3 in equation (1) we get, The above expression represents equivalent resistance of resistor in parallel. If there were n number of resistances connected in parallel, instead of three resistances, the expression of equivalent resistance would be

 

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HOPE THIS HELPS U...
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When the resistors are connected in series combination then the

equivalent resistance is Rs?= R1?+ R2?+ R3

When the resistances are connected in the parallel combination

then the equivalent resistance is

? (1 / Rp) = (1 / R1) + (1 / R2) + (1 / R3)
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V=IR Total resistance, R = R1+R2 Also, V= V1+V2
Hence, V=V1+V2
         or, IR= IR1+IR2
         or, IR=I(R1+R2)
         or, R= R1+R2

In Parallel,
I=I1+I2
V/R= V/R1+V/R2
V(1/R)=V(1/R1+1/R2)
1/R= 1/R1+1/R2
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Go
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1/Rp = 1/R1 + 1/R2 +....+1/Rn
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This is the derivation of series combination

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This is the derivation of parallel combination

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PLEASE SEE 
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When the resistors are connected in series combination then the equivalent resistance is :Rs?= R1?+ R2?+ R3

When the resistances are connected in the parallel combination

then the equivalent resistance is

? (1 / Rp) = (1 / R1) + (1 / R2) + (1 / R3)
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the above answers are really helpfull
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Please find this answer

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for series--

take 3 resistors R1, R2 and R3 connected in series and a battery of V volts has been connected. suppose the p.d across R1 is V1, R2 is V2 and R3 is V3.

total p.d across the 3 resistors should be equal to the voltage of the battery i.e.

V = V1 + V2 + V3 __________[1]

from ohm 's law--

V = IR ___________[2]

V1 = IR1 _________[3]

V2 = IR2 _________[4]

V3 = IR3 _________[5]

putting values of V1, V2 and V3 in [1]

IR = IR1 + IR2 + IR3

=IR = I [R1 + R2 + R3]

=R = R1 + R2 +R3

for parellel--

take 3 resistors R1, R2, R3 connected in parellel and connect a batery of V volts. in this case the p.d across the ends will be the same. the current flowing, however, is not the same.

total I = I1 + I2 + I3 _______[1]

from ohm 's law--

I = V / R _______[2]

I1 = V / R1 _________[3]

I2 = V / R2 __________[4]

I3 = V / R3 _________[5]

putting the values of I1, I2 and I3 in [1]

V / R = V / R1 + V / R2 + V / R3

= V / R = V [1 / R1 + 1 / R2 + 1 / R3]

= 1 / R = 1 / R1 + 1 / R2 +1 / R3

thumbx up if u wish!! :)
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for series--

take 3 resistors R1, R2 and R3 connected in series and a battery of V volts has been connected. suppose the p.d across R1 is V1, R2 is V2 and R3 is V3.

total p.d across the 3 resistors should be equal to the voltage of the battery i.e.

V = V1 + V2 + V3 __________[1]

from ohm 's law--

V = IR ___________[2]

V1 = IR1 _________[3]

V2 = IR2 _________[4]

V3 = IR3 _________[5]

putting values of V1, V2 and V3 in [1]

IR = IR1 + IR2 + IR3

=IR = I [R1 + R2 + R3]

=R = R1 + R2 +R3

 

for parellel--

take 3 resistors R1, R2, R3 connected in parellel and connect a batery of V volts. in this case the p.d across the ends will be the same. the current flowing, however, is not the same.

total I = I1 + I2 + I3 _______[1]

from ohm 's law--

I = V / R _______[2]

I1 = V / R1 _________[3]

I2 = V / R2 __________[4]

I3 = V / R3 _________[5]

putting the values of I1, I2 and I3 in [1]

V / R = V / R1 + V / R2 + V / R3

= V / R = V [1 / R1 + 1 / R2 + 1 / R3]

= 1 / R = 1 / R1 + 1 / R2 +1 / R3

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HELLO
 
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In series, the current in total circuit is same
V=IR ( According to ohm's law)
Therefore,
IR=IR1+IR2+IR3
IR=l(R1+R2+R3)
Rs=R1+R2+R3 (I is cutted)
H.p,

In parallel, the potential difference in total circuit is same.
I=V/R (According to Ohm's law)
Therefore,
V/R=V/R1+V/R2+V/R3
V(1/R)=V(1/R1+1/R2+1/R3)
1/Rp =1/R1+1/R2+1/R3 (V is cutted)
H.p,
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same ans bro
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When the resistors are connected in series combination then the

equivalent resistance is Rs = R1 + R2 + R3

When the resistances are connected in the parallel combination

then the equivalent resistance is

  (1 / Rp) = (1 / R1) + (1 / R2) + (1 / R3)

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yoyo
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u got anss
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Correct answer

When the resistors are connected in series combination then the

equivalent resistance is Rs?= R1?+ R2?+ R3

When the resistances are connected in the parallel combination

then the equivalent resistance is

? (1 / Rp) = (1 / R1) + (1 / R2) + (1 / R3)
  • 0

for series--

take 3 resistors R1, R2 and R3 connected in series and a battery of V volts has been connected. suppose the p.d across R1 is V1, R2 is V2 and R3 is V3.

total p.d across the 3 resistors should be equal to the voltage of the battery i.e.

V = V1 + V2 + V3 __________[1]

from ohm 's law--

V = IR ___________[2]

V1 = IR1 _________[3]

V2 = IR2 _________[4]

V3 = IR3 _________[5]

putting values of V1, V2 and V3 in [1]

IR = IR1 + IR2 + IR3

=IR = I [R1 + R2 + R3]

=R = R1 + R2 +R3

 

for parellel--

take 3 resistors R1, R2, R3 connected in parellel and connect a batery of V volts. in this case the p.d across the ends will be the same. the current flowing, however, is not the same.

total I = I1 + I2 + I3 _______[1]

from ohm 's law--

I = V / R _______[2]

I1 = V / R1 _________[3]

I2 = V / R2 __________[4]

I3 = V / R3 _________[5]

putting the values of I1, I2 and I3 in [1]

V / R = V / R1 + V / R2 + V / R3

= V / R = V [1 / R1 + 1 / R2 + 1 / R3]

= 1 / R = 1 / R1 + 1 / R2 +1 / R3

 

thumbx up if u wish!! :)

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answerdfh
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Input current is the current flowing through the primary windings of the transformer. The output current of a transformer is the current flowing through the output windings of it. The output winding is not physically connected to the input winding, but due to induction, a current is produced in the output wi
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Inhibited means?to prohibit from doing something.
Defeat means to conquer.
Psychology means?the mental or behavioral characteristics of an individual
Defeat Psychology is a thought process involving a loss of emotional autonomy and a sense of feeling broken or less tha
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Inhibited means?to prohibit from doing something.
Defeat means to conquer.
Psychology means?the mental or behavioral characteristics of an individual
Defeat Psychology is a thought process involving a loss of emotional autonomy and a sense of feeling broken or les
  • 0
Inhibited means?to prohibit from doing something.
Defeat means to conquer.
Psychology means?the mental or behavioral characteristics of an individual
Defeat Psychology is a thought process involving a loss of emotional autonomy and a sense of feeling broken or less th
  • 0
Inhibited means?to prohibit from doing something.
Defeat means to conquer.
Psychology means?the mental or behavioral characteristics of an individual
Defeat Psychology is a thought process involving a loss of emotional autonomy and a sense of feeling broken
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