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Electricity and Circuits

Subject: Physics
Topic: 6
Cambridge Code: 0625

Electric Charge and Current​

Charge (Q) - Property of matter (Coulombs, C)

Electric current - Rate of charge flow

I=QtI = \frac{Q}{t}

Where:

  • I = current (Amperes, A)
  • Q = charge (Coulombs, C)
  • t = time (seconds)

Conventional Current​

Conventional current - Flows from positive to negative

(Actually electrons flow negative to positive, opposite direction)

Potential Difference​

Potential difference (V) - Energy per unit charge

V=WQV = \frac{W}{Q}

Where:

  • W = work (Joules)
  • Q = charge (Coulombs)
  • Unit: Volts (V) = J/C

E.m.f. (ε) - Potential difference from source

Terminal p.d. - Voltage available to circuit (less than e.m.f. if internal resistance)

Vterminal=ε−IrV_{\text{terminal}} = ε - Ir

Where r = internal resistance

Resistance​

Resistance (R) - Opposition to current

R=VIR = \frac{V}{I}

Unit: Ohms (Ω)

Ohm's Law​

For ohmic conductors: V=IRV = IR

V-I graph: straight line through origin

  • Resistance constant
  • Temperature must be constant
  • Examples: resistors, wires (at constant T)

Factors Affecting Resistance​

R=ρLAR = ρ\frac{L}{A}

Where:

  • ρ = resistivity (material property)
  • L = length
  • A = cross-sectional area

Effect of changes:

  • Longer wire → higher R
  • Wider wire → lower R
  • Higher temperature → higher R (usually)

Circuit Analysis​

Series Circuits​

Components in line, single path

Current: Itotal=I1=I2=I3I_{\text{total}} = I_1 = I_2 = I_3 (same everywhere)

Voltage: Vtotal=V1+V2+V3V_{\text{total}} = V_1 + V_2 + V_3

Resistance: Rtotal=R1+R2+R3R_{\text{total}} = R_1 + R_2 + R_3

Parallel Circuits​

Components with multiple paths

Current: Itotal=I1+I2+I3I_{\text{total}} = I_1 + I_2 + I_3

Voltage: Vtotal=V1=V2=V3V_{\text{total}} = V_1 = V_2 = V_3 (same across each)

Resistance: 1Rtotal=1R1+1R2+1R3\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}

For two resistors: Rtotal=R1R2R1+R2R_{\text{total}} = \frac{R_1R_2}{R_1 + R_2}

Energy and Power​

Power Dissipated​

P=IV=I2R=V2RP = IV = I^2R = \frac{V^2}{R}

Where:

  • P = power (Watts, W)
  • I = current
  • V = voltage
  • R = resistance

Energy Transferred​

E=Pt=IVtE = Pt = IVt

Unit: Joules (J) or kilowatt-hours (kWh)

Cost calculation: Cost=Power (kW)×Time (h)×Rate (£/kWh)\text{Cost} = \text{Power (kW)} × \text{Time (h)} × \text{Rate (£/kWh)}

Efficiency​

η=Useful power outputTotal power inputη = \frac{\text{Useful power output}}{\text{Total power input}}

Cells and E.m.f.​

E.m.f. (ε) - Energy per unit charge from cell

ε=WQε = \frac{W}{Q}

Terminal p.d. - Voltage measured across cell terminals

V=ε−IrV = ε - Ir

Where r = internal resistance of cell

Short circuit: r very small, current very large

Kirchhoff's Laws​

First Law (Current Conservation)​

Sum of currents in = Sum of currents out at junction

∑Iin=∑Iout\sum I_{\text{in}} = \sum I_{\text{out}}

Second Law (Voltage Loop)​

Sum of e.m.f. = Sum of p.d. around closed loop

∑ε=∑IR\sum ε = \sum IR

Going around loop:

  • Resistance increases p.d. (voltage drop)
  • Source increases potential

Measuring Instruments​

Ammeter​

  • Measures current
  • Connected in series
  • Low resistance
  • Ideal: R ≈ 0 Ω

Voltmeter​

  • Measures potential difference
  • Connected in parallel
  • High resistance
  • Ideal: R ≈ ∞ Ω

Rheostat (Variable Resistor)​

  • Changes circuit resistance
  • Adjusts current

Electromotive Force and Internal Resistance​

Real source has internal resistance

Circuit equation: ε=I(R+r)ε = I(R + r)

Where R = external resistance, r = internal resistance

Terminal voltage: V=ε−Ir=IRV = ε - Ir = IR

As current increases:

  • Voltage drop across r increases
  • Terminal voltage decreases

Key Points​

  1. Current = charge/time
  2. Potential difference = energy/charge
  3. Resistance opposes current
  4. Ohm's law: V = IR
  5. Series: currents equal, voltages add
  6. Parallel: voltages equal, currents add
  7. Power = IV = I²R = V²/R
  8. E.m.f. minus internal resistance = terminal voltage
  9. Two laws: Current conservation, voltage loop
  10. Ammeter in series, voltmeter in parallel

Practice Questions​

  1. Calculate current using I = Q/t
  2. Apply Ohm's law
  3. Analyze series circuits
  4. Analyze parallel circuits
  5. Calculate power dissipated
  6. Calculate energy transferred
  7. Apply Kirchhoff's laws
  8. Account for internal resistance
  9. Solve complex circuits
  10. Calculate costs

Revision Tips​

  • Draw clear circuit diagrams
  • Label all components
  • Apply Ohm's law carefully
  • Distinguish series and parallel
  • Remember resistance combination rules
  • Calculate power correctly
  • Understand internal resistance effect
  • Practice Kirchhoff's laws
  • Check units always
  • Verify using energy conservation