Current Electricity – Quick Revision Notes

Importance of Electricity

  • Essential for daily life, industry, medicine, appliances
  • Natural sources: electric eels, lightning; human body conducts electricity

Electric Potential & Potential Difference

  • Electric charge flows from higher to lower potential (water-level analogy)
  • Potential difference (p.d.) definition: V=W/QV = W/Q
    • VV: volt (unit) WW: work (joule) QQ: charge (coulomb)
  • Unit scale: 1 mV=10−3 V1\,\text{mV}=10^{-3}\,\text{V}, 1\,\text{\mu V}=10^{-6}\,\text{V}, 1 kV=103 V1\,\text{kV}=10^{3}\,\text{V}, 1 MV=106 V1\,\text{MV}=10^{6}\,\text{V}

Electric Current

  • Current = flow of charge: I=Q/tI = Q/t
  • Unit: ampere (A); 1 A=1 C s−11\,\text{A}=1\,\text{C s}^{-1}
  • Sub-units: 1 mA=10−3 A1\,\text{mA}=10^{-3}\,\text{A}, 1\,\text{\mu A}=10^{-6}\,\text{A}
  • Direction: electrons (−→+)(- \to +), conventional current (+→−)(+ \to -)

Resistance & Ohm’s Law

  • Resistance opposes current flow
  • Ohm’s law (constant physical conditions): V=IRV = I R ⇒ I=V/RI = V/R
  • Resistance factors: R=ρL/AR = \rho L/A
    • LL↑ ⇒ RR↑ • AA↑ ⇒ RR↓ • Material (ρ) • Temperature (usually RR↑)
  • Unit: ohm (Ω); 1 Ω=1 V A−11\,\Omega = 1\,\text{V A}^{-1}

Conductors vs Insulators

  • Conductors: very low RR (Cu, Al, Fe, Ag) → wiring
  • Insulators: very high RR (rubber, glass, plastic, wood) → safety

Resistivity Reference (≈Ω m\Omega\,\text{m})

  • Cu 1.7×10−81.7\times10^{-8}, Al 2.8×10−82.8\times10^{-8}, Fe 1.0×10−71.0\times10^{-7}
  • Nichrome 1.1×10−61.1\times10^{-6} (alloy)
  • Glass/Rubber 1012−101610^{12}-10^{16} (insulators)

Circuit Symbols

  • Cell, battery, resistor, switch, ammeter (A), voltmeter (V), bulb (\ud83d\udca1)

Series Connection

  • One path; current same: I<em>1=I</em>2=I3I<em>1=I</em>2=I_3
  • p.d. splits: V=V<em>1+V</em>2+V3V = V<em>1+V</em>2+V_3
  • Total resistance: R<em>s=∑R</em>iR<em>s = \sum R</em>i
  • Failure of one ⇒ all stop; bulbs dimmer

Parallel Connection

  • Junction branches; p.d. same: V<em>1=V</em>2=V3V<em>1=V</em>2=V_3
  • Current splits: I=∑IiI = \sum I_i
  • Total resistance: 1/R<em>p=∑1/R</em>i1/R<em>p = \sum 1/R</em>i
  • Failure of one ≠ others; bulbs normal brightness

Domestic Wiring (India)

  • Live (red/brown), neutral (blue/black) ⇒ 220 V220\,\text{V} difference
  • Earth (yellow/green) for safety
  • All appliances in parallel; fuse melts at excess II

Core Safety Rules

  • Dry hands; rubber-soled shoes
  • Switch off before servicing; use wooden pole for shock victim

Key Formulas (Quick-view)

  • Potential difference: V=W/QV = W/Q
  • Current: I=Q/tI = Q/t
  • Ohm’s law: V=IRV = I R
  • Resistance: R=ρL/AR = \rho L/A
  • Series: R<em>s=R</em>1+R<em>2+R</em>3+…R<em>s = R</em>1+R<em>2+R</em>3+\dots
  • Parallel: 1/R<em>p=1/R</em>1+1/R<em>2+1/R</em>3+…1/R<em>p = 1/R</em>1+1/R<em>2+1/R</em>3+\dots

Sample Calculations

  • Charge flow: I=0.4 A,  t=5 min=300 s⇒Q=It=120 CI=0.4\,\text{A},\; t=5\,\text{min}=300\,\text{s}\Rightarrow Q=I t=120\,\text{C}
  • Current through bulb: V=230 V,  R=1000 Ω⇒I=0.23 AV=230\,\text{V},\; R=1000\,\Omega\Rightarrow I=0.23\,\text{A}
  • Series resistors: 15 Ω+3 Ω+4 Ω=22 Ω15\,\Omega+3\,\Omega+4\,\Omega=22\,\Omega

Memory Triggers

  • Ohm’s triangle: VV top, II & RR bottom
  • Series: “same II, VV splits”; Parallel: “same VV, II splits”
  • Resistance trend: L↑⇒R↑L \uparrow \Rightarrow R \uparrow, A↑⇒R↓A \uparrow \Rightarrow R \downarrow
  • Current direction: electrons (−→+)(- \to +), conventional (+→−)(+ \to -)

Common Pitfalls

  • Don’t mix electron & conventional directions
  • RR increases with LL and temperature
  • In parallel, RpR_p < smallest individual RR
  • Always check units before final answer