**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 =**

**I**

_{1}**=**

**I**

_{2}**=**

**I**

_{3}**=…**;

**(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 =****R**_{1}**+****R**_{2}**+****R**_{3 ...}**(Also confirmed by: IR = IR**_{1}+ IR_{2}+ IR_{3}+ …).
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:__Potential difference (PD a.k.a. V)__:

i.

**SAME PD**(potential difference) across separate pathways:**V = V**;_{1}= V_{2}= …
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)**__Current (I):__

i.
The

**SUM of currents**in separate pathways =**Total current**leaving or returning to cell:**I = I**;_{1}+ I_{2}+ I_{3}+ …
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/R**

_{1}+ V/R_{2}+ V/R_{3}**+ …**(This leads us to the equation for effective resistance in a parallel circuit:

**1/R = 1/R**)

_{1}+ 1/R_{2}+ 1/R_{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/R**

_{1}+ 1/R_{2}+ 1/R_{3}+ …
(From:

**V/R = V/R**_{1}+ V/R_{2}+ V/R_{3}**+ …**, 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)****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.

__----------------------------------------------------------------------------------__

__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)

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