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#### 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
1. Calculate the current in each of the resistors • Using Kirchhoff’s first law:
• I3 = I1 + I2
• Using Kirchhoff’s second law on loop ABEF:
• 3 = 30I3 + 10I1
• Using Kirchhoff’s second law on loop CBED:
• 2 = 30I3
• Using Kirchhoff’s second on loop ACDF:
• 3 – 2 = 10I1
• Solve the simultaneous equations:
• I1 = 0.1
• I2 = -0.033
• I3 = 0.067
###### Deriving Effective Resistance in Series
• From Kirchhoff’s second law:
• E = ∑IR
• IR = IR1 + IR2
• Current is constant, therefore:
• R = R1 + R2
###### Deriving Effective Resistance in Parallel
• From Kirchhoff’s first law:
• I = ∑I
• I = I1 + I2
• 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 R1:
• Resistance decreases with increasing temperature
• It can be used in potential divider circuits to monitor and control temperatures
• Usage of an LDR at R1:
• 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:
1. E1 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 E2 • E1/E2 = L1/L2
• 10/E2 = 1/0.4
• E2 = 4 V
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