Series and Parallel Circuits

1.      What is an electrical circuit?

a.      An electric circuit is the path or network of paths formed by electrical components through which electric current flows when the circuit is closed.

b.      Electrical components that form a circuit with an electric source include:

                          i.      Resistor

                        ii.      Lamp

                      iii.      Switch

                      iv.      Electrical appliances

                        v.      Connecting wires

c.       Internal and external circuits:

                          i.      Internal circuit refers to the path taken by the current within the source (cell, battery, etc.).

                        ii.      External circuit refers the path taken by the current outside the source.

d.      Series and parallel circuits are 2 basic ways of connecting electrical components to form circuits for the current to flow.

2.      A series circuit refers to the single path formed by electrical components which are connected end to end consecutively to an electric source.

3.      In a series circuit, experimental evidence (at pg. 368) shows that:

a.       Potential difference (PD a.k.a. V):

                                       i.      PD applied across the external circuit = the SUM of individual PDs across each external component: V = V1 + V2 + V3 +…;

                                     ii.      In other words, the external components share the applied voltage across the external circuit;

                                    iii.      The electromotive force V(e.m.f.) or E of the cell (or battery) = the Sum of individual PDs across all components (including across the cell): V(e.m.f.) = V(drop) + V1 + V2 + …

                                   iv.      In other words, all the components in the circuit (incl. the cell) share the V(e.m.f.) of the cell.

b.      Current (I)

      SAME current flows through all the components: I = I₁ = I₂ = I₃ =…;

(Yr 2006 SPM P1 Q42 at pg. 58)

(Yr 2009 SPM P1 Q38 at pg. 194)

(Yr 2010 SPM P1 Q39 at pg. 240)

c.       Resistance (R):

                                       i.      Effective Resistance = the SUM of individual resistance of each component: R = R₁ + R₂ + R_3 ... (Also confirmed by: IR = IR₁ + IR₂ + IR₃ + …).

                                     ii.      In other words:

1.      the effective resistance R in a series circuit is larger than each of the individual resistor;

2.      the combination of resistors in series effectively forms a longer resistor with higher resistance

                  (Yr 2006 SPM P1 Q39 at pg. 57)

4.      A parallel circuit refers to the network of separate and parallel paths formed by electrical components which are connected side by side and their corresponding ends are joined together to an electric source, a cell or a battery.

5.      In a parallel circuit, experimental evidence (at pg. 368) shows that:

1. Potential difference (PD a.k.a. V):

                                                               i.      SAME PD (potential difference) across separate pathways: V = V₁ = V₂ = …;

                                                             ii.      In other words, voltage across each resistor in parallel is the same.

   (Yr 2005 SPM P1 Q43 at pg. 13)

(Yr 2007 SPM P1 Q36 at pg. 99)

2. Current (I):

                                                               i.      The SUM of currents in separate pathways = Total current leaving or returning to cell: I = I₁ + I₂ + I₃ + …;

                                                             ii.      In other words, resistors in parallel share the main current.

                                                            iii.      As current in each pathway is given by V/R, and V is the same for all pathways, therefore, main current = sum of individual currents also means:

               V/R = V/R₁ + V/R₂ + V/R₃ + … (This leads us to the equation for effective resistance in a parallel circuit: 1/R = 1/R₁ + 1/R₂ + 1/R₃ + …)

3. Resistance (R):

                                                               i.      Effective resistance of resistors in parallel is given by: The reciprocal of the effective resistance = sum of the reciprocals of individual resistance in each pathway:

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

               (From: V/R = V/R₁ + V/R₂ + V/R₃ + …, please see 5b(iii).)

            (Yr 2008 SPM P1 Q36 at pg. 147)

                                                             ii.      In other words:

1.      the effective resistance R in a parallel circuit is smaller than each of individual resistor;

2.      the combination of resistors in parallel effectively forms a resistor with larger cross-sectional area and therefore lower combined resistance.

                                                            iii.      When identical resistors are in parallel:

1.      Quick Formula to Calculate Effective Resistance:

      R(effective) = R(individual)/n

      Where, n = number of identical resistors in parallel

(Yr 2006 SPM P1 Q38 at pg. 57)

(Yr 2008 SPM P1 Q37 at pg. 148)

(Yr 2011 SPM P2 Q6 at pg. 301~302)

6. Combined circuit refers to a circuit with series and parallel arrangements of components.

(Yr 2010 SPM P1 Q40 at pg. 241)

(Yr 2010 SPM P2 CQ12(b) at pg. 264~266)

Summary:

Ohm's law states that the current flowing, I through an ohmic conductor (pure metal) is directly proportional the potential difference, V across the conductor if the temperature remains constant.

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Example how to determine effective resistance of a parallel circuit:

• When resistors are connected in parallel, the effective resistance becomes smaller compare to that of connection in series.
• Thus, if terminal voltage Vt is the same, a higher main current will be shared by the individual resistors in parallel - thus each resistor will receive higher flow of current thereby producing a brighter bulb in parallel circuit
  
  

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Updated by: tutortan1@gmail.com (25/05/16)