PhysicsVery High Weightage β
β
β
β
β
Class 12
Current Electricity
Ohm's law, Kirchhoff's laws, Wheatstone bridge, potentiometer, and cells β the most numerical chapter in electricity. Expect 4β5 EAPCET questions.
4β5Questions in EAPCET
~5%Paper Weightage
12Core Formulas
4Mistake Traps
Concept Core
From Ohm's Law to Kirchhoff's laws β mastering circuits.
Ohm's Law & Resistance
V = IR. Resistance R = ΟL/A (Ο = resistivity, L = length, A = cross-section).
Series: R_eff = Rβ + Rβ + ... (same current; voltage divides)
Parallel: 1/R_eff = 1/Rβ + 1/Rβ + ... (same voltage; current divides)
Temperature: R = Rβ(1 + Ξ±T) where Ξ± = temperature coefficient of resistance. For metals Ξ± > 0 (resistance increases with T). For semiconductors/NTC: Ξ± < 0.
Kirchhoff's Laws
KCL (Junction Rule): Sum of currents entering a junction = sum of currents leaving. Ξ£I_in = Ξ£I_out (conservation of charge)
KVL (Loop Rule): Sum of EMFs and potential drops around any closed loop = 0. Ξ£E = Ξ£IR (conservation of energy)
Wheatstone Bridge
For a balanced Wheatstone bridge: no current through galvanometer, and:
P/Q = R/S (balanced condition)
Applications: measurement of unknown resistance. Metre bridge uses a uniform wire: P/Q = l/(100βl) where l is balance point length from left end.
EMF, Internal Resistance & Cells
A cell with EMF Ξ΅ and internal resistance r:
Terminal voltage V = Ξ΅ β Ir (discharging)
V = Ξ΅ + Ir (charging)
Current I = Ξ΅/(R+r)
Cells in series: Ξ΅_eff = Ξ΅β+Ξ΅β, r_eff = rβ+rβ
Cells in parallel: Ξ΅_eff = Ξ΅β = Ξ΅β (if equal), r_eff = r/n
Power & Electrical Energy
P = VI = IΒ²R = VΒ²/R
Energy = Pt = VIt = IΒ²Rt
Maximum power transfer: Maximum power delivered to external resistance R when R = r (internal resistance). P_max = Ρ²/(4r)
Potentiometer
Used to compare EMFs and find internal resistance. Key principle: no current is drawn when balance is achieved β accurate measurement.
Ξ΅β/Ξ΅β = lβ/lβ (balance lengths)
r = R(lββlβ)/lβ (internal resistance)
Formula Vault
All current electricity formulas β circuits, cells, and measurements.
Ohm's Law
V = IR
V in volts; I in amps; R in ohms
Resistance
R = ΟL/A
Ο = resistivity; L = length; A = area
Series Resistors
R_eff = Rβ + Rβ + ...
Same current; voltage divides
Parallel Resistors
1/R_eff = 1/Rβ + 1/Rβ
Same voltage; current divides
Cell Terminal Voltage
V = Ξ΅ β Ir (discharging)
V = Ξ΅ + Ir when charging
Cell Current
I = Ξ΅/(R + r)
R = external resistance
Wheatstone Balance
P/Q = R/S
No current through galvanometer
Metre Bridge
P/Q = l/(100βl)
l = balance length from left
Power
P = VI = IΒ²R = VΒ²/R
Three equivalent forms
Max Power Transfer
P_max = Ρ²/4r when R=r
R = r for maximum power to load
Potentiometer EMF ratio
Ξ΅β/Ξ΅β = lβ/lβ
l = balance length
KVL
Ξ£E = Ξ£IR around loop
Signs: EMF and IR in same direction β positive
Worked Examples
5 problems β series/parallel, cell with internal resistance, Wheatstone, KVL, and power.
EasyThree resistors 2Ξ©, 3Ξ©, 6Ξ© in parallel β find equivalentβΎ
Find equivalent resistance of 2Ξ©, 3Ξ©, and 6Ξ© resistors in parallel.
1
1/R_eff = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1
β R_eff = 1 Ξ©
EasyCell with Ξ΅=12V, r=2Ξ©, R=10Ξ© β find terminal voltageβΎ
A cell of EMF 12V and internal resistance 2Ξ© is connected to 10Ξ© external. Find terminal voltage.
1
I = Ξ΅/(R+r) = 12/12 = 1 A
2
Terminal voltage V = Ξ΅ β Ir = 12 β 1Γ2 = 10 V
β Terminal voltage = 10 V
MediumWheatstone bridge: P=10Ξ©, Q=20Ξ©, R=15Ξ© β find balanced SβΎ
In a Wheatstone bridge, P = 10Ξ©, Q = 20Ξ©, R = 15Ξ©. Find S for balance.
1
Balance condition: P/Q = R/S β S = QR/P = 20Γ15/10 = 30 Ξ©
β S = 30 Ξ©
EAPCET LevelApply KVL to find current in a loop with two cellsβΎ
In a loop: cell 1 (Ξ΅=10V, r=1Ξ©) and cell 2 (Ξ΅=4V, r=1Ξ©) connected in series with R=5Ξ©. Cells oppose each other. Find current.
1
Assign current I clockwise. Apply KVL around loop:
2
10 β 4 β I(1) β I(5) β I(1) = 0
3
6 β 7I = 0 β I = 6/7 β 0.86 A
β I = 6/7 A β 0.86 A
Trap QuestionMaximum power to external resistance when R = 0 (short circuit)?βΎ
A student claims maximum power to external R occurs when R = 0 (short circuit current maximises I). Is this correct?
1
The trap: Maximum current (at R=0) doesn't mean maximum power to R.
2
P_external = IΒ²R = [Ξ΅/(R+r)]Β² Γ R
3
At R=0: P = 0 (zero voltage across zero resistance)
4
At R=β: P = 0 (zero current through infinite resistance)
5
Maximum P occurs when dP/dR = 0 β solving gives R = r.
6
P_max = Ρ²/(4r) when R = r (external matches internal resistance)
β Maximum power when R = r (not R = 0); P_max = Ρ²/(4r)
Mistake DNA
4 circuit errors from EAPCET distractor analysis.
π
Applying Series Formula to Parallel Resistors (And Vice Versa)
The most common circuit error. Series and parallel combination formulas are frequently swapped.
β Wrong
Parallel: R = Rβ+Rβ β
(that's series!)
Series: 1/R=1/Rβ+1/Rβ β
β Correct
Series: R = Rβ+Rβ β
Parallel: 1/R=1/Rβ+1/Rβ β
Check: parallel R < smallest R
Quick check: parallel resistance is ALWAYS less than the smallest individual resistance. If your answer is larger, you used the wrong formula.
β‘
Terminal Voltage = EMF (Ignoring Internal Resistance)
A real cell has internal resistance r. Terminal voltage is less than EMF when current flows.
β Wrong
Terminal voltage =
EMF = 12V β
(only when I=0 or r=0)
β Correct
V = Ξ΅ β Ir β
= 12 β IΓr < 12
V = Ξ΅ only when open
circuit (I=0)
Terminal voltage equals EMF only when the circuit is open (no current). When current flows, voltage drops across internal resistance r.
π
KVL: Wrong Signs for EMF and Resistance
In KVL, sign conventions for EMF and IR drops must be consistent with the chosen loop direction.
β Wrong
Traversing against current
I: add +IR (wrong sign) β
Traversing into β terminal
of cell: add +Ξ΅ β
β Correct
Against current: βIR β
With current: +IR β
Into + terminal: +Ξ΅ β
Into β terminal: βΞ΅ β
KVL sign convention: moving in direction of assumed current β voltage drop βIR. Moving from β to + inside the cell β EMF +Ξ΅. Be consistent with loop direction.
βοΈ
Max Power Transfer: Maximum Current = Maximum Power to R
P_external = IΒ²R. Maximum I (when R=0) gives I_max but P = IΒ²Γ0 = 0. Maximum P requires balancing I and R.
β Wrong
Max P at R=0 (short circuit)
I = Ξ΅/r maximum β
P = IΒ²Γ0 = 0 W β
β Correct
Max P_external when R=r β
P_max = Ρ²/(4r) β
Derivative condition:
dP/dR = 0 β R = r
Power to R is P = [Ξ΅/(R+r)]Β²ΓR. This is zero at R=0 and R=β, maximum somewhere in between. Differentiating and setting to zero gives R = r.
Chapter Intelligence
Current electricity is the most tested chapter in Class 12 Physics β numerical mastery is essential.
EAPCET Weightage (2019β2024)
Cell with internal resistance~7 Wheatstone bridge / metre bridge~5 High-Yield PYQ Patterns
Equivalent resistance of combinationTerminal voltage of cellFind R for balanced bridgeKVL: current in two-cell loopMaximum power condition R=rPotentiometer balance length ratioResistance from resistivity formula
Exam Strategy
- Circuit simplification: first identify series/parallel relationships visually. Redraw the circuit if needed. Work from innermost combination outward.
- Cell problems: always use V = Ξ΅ β Ir (not V = Ξ΅). The voltage drop Ir across internal resistance is often the key to the answer.
- KVL: choose a loop direction, apply the sign convention consistently. Sum = 0. Two unknowns β two loops β two equations.
- Maximum power transfer: R = r. This appears as both a formula question and a conceptual question. Know both forms: P_max = Ρ²/(4r).
- Current electricity links to Magnetism (magnetic force on current-carrying conductor) and Electromagnetic Induction (changing current creates changing B β EMF).
β EAMCET Hub
FREE
vidhyapath.com β