Current Electricity Revision Notes (NEET)

Ohm & Resistance

• $V = IR$; $R = \rho L/A$; specific resistance depends on material and T.
• Temperature coefficient: $R_T = R_0(1 + \alpha \Delta T)$.
• Series: $R = R_1 + R_2$; Parallel: $1/R = \sum 1/R_i$.
• Drift velocity $v_d = eE\tau/m$; $I = neA v_d$; mobility $\mu = v_d/E$.

Kirchhoff's Laws

• KCL: $\sum I = 0$ at junction.
• KVL: $\sum V = 0$ around loop.

Circuits

• Cells in series: $E = E_1 + E_2$, $r = r_1 + r_2$.
• Parallel: $E/r = \sum E_i/r_i$; $1/r = \sum 1/r_i$.
• Wheatstone bridge (balanced): $P/Q = R/S$; no current in galvanometer.
• Metre bridge: $R/S = l/(100-l)$.

Potentiometer

• Compares EMFs: $E_1/E_2 = l_1/l_2$.
• Internal resistance: $r = R(l_1 - l_2)/l_2$.

Power & Heating

• $P = VI = I^2 R = V^2/R$.
• Heat $H = I^2 R t$ (Joule's law).
• Home power in kWh; unit rate calculations for bills.

Meters

• Ammeter: low R in shunt; galvanometer + shunt $S = I_g G/(I − I_g)$.
• Voltmeter: high R in series; $R = V/I_g − G$.

Extra

• EMF vs terminal voltage: $V = E - Ir$ (during discharge); $V = E + Ir$ (charging).
• Colour code (BBROY-GBV-GW): 0-9; tolerance gold ±5%, silver ±10%.
• Junction potential in semiconductors — see semiconductor chapter for extension.

Practice MCQs

Q1. Resistance of a wire is doubled when its length is doubled at same area if resistivity is constant. New resistance is A) Same B) 2R C) 4R D) R/2

Q2. Drift velocity for I=1A, n=10²⁸/m³, A=10⁻⁶ m² is (in m/s) A) 6.25×10⁻⁴ B) 1.6×10⁻¹⁹ C) 6.25×10⁻⁵ D) 1

Q3. A Wheatstone bridge is balanced when P=Q=R=10Ω and S= A) 10 B) 20 C) 5 D) 1

Q4. Three 6Ω resistors in parallel give A) 18Ω B) 6Ω C) 2Ω D) 3Ω

Q5. Two identical cells (EMF E, r) in parallel across R give current A) E/(R+r) B) 2E/(R+r/2) C) E/(R+r/2) D) E/(R+2r)

Q6. Kirchhoff's junction rule is based on conservation of A) Energy B) Charge C) Momentum D) Mass

Q7. Power dissipated in R=10Ω with V=20V is A) 4W B) 10W C) 40W D) 400W

Q8. Potentiometer is used to compare EMFs because it A) Draws no current B) Has high resistance C) Is portable D) Is cheap

Q9. A 20Ω galvanometer full-scale at 1 mA. Shunt to make ammeter of 1A range is A) 0.02Ω B) 0.2Ω C) 2Ω D) 20Ω

Q10. Terminal voltage of a discharging cell is A) E + Ir B) E − Ir C) IR D) 0

Answers: 1-B (R ∝ L.), 2-C (v=I/(neA) = 1/(1.6×10⁻¹⁹ × 10²⁸ × 10⁻⁶)=6.25×10⁻⁵ (approx).), 3-A (P/Q=R/S → S=10.), 4-C (6/3 = 2Ω.), 5-C (Parallel: E_eff=E, r_eff=r/2.), 6-B (Charge conservation.), 7-C (V²/R = 400/10 = 40W.), 8-A (Null method → no current drawn from source.), 9-A (S=IgG/(I−Ig) ≈ 0.02Ω.), 10-B (V=E−Ir during current flow.)

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