PHY 193 Resistors In Series And Parallel

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PHYSICS FOR ENGINEERING II

Learning Outcome

1) To determine the combination of resistors in series and/or parallel

2) To calculate the equivalent resistance for the combination

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Resistors In Series

The symbol of resistor in an electrical circuit:

Two resistors are said to be in series whenever the same

current physically flows through both of the resistors.

R 1

R 2

I

I

R 1

R 2

I

I

R 1 R 2

I I

R 1

R 2

I

I

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Characteristics Of Resistors In Series

The same current same current II flows through each resistor flows through each resistor where

Assuming that the connecting wires have no resistanceAssuming that the connecting wires have no resistance, the total potential difference, V is given by

… (1) From the definition of resistance, thus

321 IIII

321 VVVV

2 2;V IR 3 3;V IR1 1;V IR eqV IR

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Characteristics Of Resistors In SeriesSubstituting for V1, V2 , V3 and V in the eq. (1) gives

… (2)

where

e q 1 2 3 I R I R I R I R

eq 1 2 3R R R R

eq : equivalent resistanceR

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Resistors In ParallelTwo resistors are said to be in parallel when the different

current flows through both of the resistors.

V

1R

3R

2R

I I

2I

1I

3I

1V2V

3VV 1R 3R

2R

I

I

1I

3I

2I

2V

3V

1V

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There same potential difference, same potential difference, VV across each resistor across each resistor where

The charge is conservedcharge is conserved, therefore the total current I in the circuit is given by

… (3) From the definition of resistance, thus

Characteristics Of Resistors In Parallel

321 VVVV

321 IIII

22

;V

IR

33

;V

IR

11

;V

IR

eq

VI

R

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Characteristics Of Resistors In ParallelSubstituting for I1, I2 , I3 and I in the eq. (3) gives

… (4)

1 2 3eq

V V V V

R R R R

eq 1 2 3

1 1 1 1

R R R R

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a) Are R3 and R4 in series and why? - Yes because the same current flows through both of

the resistors. b) Which resistors are in parallel?

- R1 and R3 AND R2 and R3

R 1

R 3

R 4

R 2

I 1

I 2I 3

I 3

Example 1:

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Example 2:

Calculate:a) The equivalent resistance of the circuit,b) The current passes through the 12 resistor,c) The potential difference across 4.0 resistor,The internal resistance of the battery may be ignored.Ans:

0.4

0.2

V 0.8

12

eq 1.78 R A 50.02 I V 0.21 V

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Exercise:

For the circuit above, calculate the effective resistance betweenthe points A and B.

Ans:

0.5

10 10

A

B

0.5

20

eq 7.14 R

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References:

Young, Freedman (2003), University Physics, 9th Edition, Pearson Addison Wesley

Giambattista, Richardson, Richardson (2007), College Physics, 2nd Edition, McGraw Hill International Edition

Cheong Foon Choong (2008), Pre-U Text STPM Physics Volume 1, Pearson Longman

Frederick J. Bueche, Eugene Height (1988), College Physics, 10th Edition, McGraw Hill

Arthur Beiser (1988), Applied Physics, 4th Edition, McGraw Hill

Cheong Foon Choong (2008), Q & A STPM Physics (960) Paper 2 (Volume 1), Pearson Longman