#### DC Circuits

- Electromotive force is the energy converted into electrical energy when 1 C of charge passes through the power source

**P.D. and E.M.F.**

**Internal Resistance**

- Internal resistance is the resistance to current flow within the power source; it reduced p.d. when delivering current

- V = Ir – E
- Voltage across the resistor: V = IR
- Voltage lost to internal resistance: V = Ir
- Thus e.m.f.: E = IR + Ir
- E = I(R + r)

**Kirchhoff’s First Law**

- Sum of currents into a junction is equal to the sum of currents out of the junction
- Kirchhoff’s first law is another statement of the law of conservation of charge

**Kirchhoff’s Second Law**

- Sum of e.m.fs in a closed circuit is equal to the sum of the potential differences
- Kirchhoff’s second law is another statement of the law of conservation of energy

**Applying Kirchhoff’s Laws**

- Calculate the current in each of the resistors

- Using Kirchhoff’s first law:
- I
_{3}= I_{1}+ I_{2}

- I
- Using Kirchhoff’s second law on loop ABEF:
- 3 = 30I
_{3}+ 10I_{1}

- 3 = 30I
- Using Kirchhoff’s second law on loop CBED:
- 2 = 30I
_{3}

- 2 = 30I
- Using Kirchhoff’s second on loop ACDF:
- 3 – 2 = 10I
_{1}

- 3 – 2 = 10I
- Solve the simultaneous equations:
- I
_{1}= 0.1 - I
_{2}= -0.033 - I
_{3}= 0.067

- I

- Using Kirchhoff’s first law:

**Deriving Effective Resistance in Series**

- From Kirchhoff’s second law:
- E = ∑IR
- IR = IR
_{1}+ IR_{2}

- Current is constant, therefore:
- R = R
_{1}+ R_{2}

- R = R

**Deriving Effective Resistance in Parallel**

- From Kirchhoff’s first law:
- I = ∑I
- I = I
_{1}+ I_{2} ^{V}/_{R}=^{V}/_{R1}+^{V}/_{R2}

- Voltage is constant, therefore;
^{1}/_{R}=^{1}/_{R1}+^{1}/_{R2}

**Properties of Magnets**

- A potential divider divides the voltage into smaller parts

^{Vout}/_{Vin}=^{R2}/_{RTotal}

- Usage of a thermistor at R
_{1}:- Resistance decreases with increasing temperature
- It can be used in potential divider circuits to monitor and control temperatures

- Usage of an LDR at R
_{1}:- Resistance decreases with increasing light intensity
- It can be used in potential divider circuits to monitor light intensity

**Potentiometers**

- A potentiometer is a continuously variable potential divider used to compare potential differences
- Potential difference along the wire is proportional to the length of the wire
- It can be used to determine the unknown e.m.f. of a cell
- This can be done by moving the sliding contact along the wire until it finds the null point that the galvanometer shows a zero reading; the potentiometer is balanced
- For example:
- E
_{1}is 10 V, distance XY is equal to 1 m. The potentiometer is balanced at point T which is 0.4 m from X. Calculate E_{2}

^{E1}/_{E2}=^{L1}/_{L2}^{10}/_{E2}=^{1}/_{0.4}- E
_{2}= 4 V

- E