Is it correct to say: Confusing EMF (ε) with terminal potential difference (V)?

V = ε − Ir. When current flows, V < ε; only in open circuit V = ε.

Is it correct to say: Using KVL without a consistent sign convention?

Fix a direction of traversal. EMF rise = +, EMF drop = −; resistor drop in direction of current = −.

Is it correct to say: Assuming Wheatstone bridge is balanced whenever galvanometer shows a small current?

Balance means EXACTLY zero galvanometer current. Otherwise not balanced.

Is it correct to say: Applying ρ = R·A/l with A in mm² and l in cm?

Convert all to SI: metres and m². Otherwise ρ is off by many orders of magnitude.

Is it correct to say: Assuming drift velocity is close to electron thermal speed?

v_d is typically 10⁻⁴ m/s — very small. Thermal speed is 10⁶ m/s. Do not confuse.

Is it correct to say: Forgetting factor of internal resistance in potentiometer internal-resistance formula?

Use r = R[(l₁ − l₂)/l₂] where R is the shunt resistance. Do not swap l₁ and l₂.

Current Electricity

Q: Is it correct to say: Using KVL without a consistent sign convention?

Fix a direction of traversal. EMF rise = +, EMF drop = −; resistor drop in direction of current = −.

Q: Is it correct to say: Assuming Wheatstone bridge is balanced whenever galvanometer shows a small current?

Balance means EXACTLY zero galvanometer current. Otherwise not balanced.

Q: Is it correct to say: Applying ρ = R·A/l with A in mm² and l in cm?

Convert all to SI: metres and m². Otherwise ρ is off by many orders of magnitude.

Q: Is it correct to say: Assuming drift velocity is close to electron thermal speed?

v_d is typically 10⁻⁴ m/s — very small. Thermal speed is 10⁶ m/s. Do not confuse.

Q: Is it correct to say: Forgetting factor of internal resistance in potentiometer internal-resistance formula?

Use r = R[(l₁ − l₂)/l₂] where R is the shunt resistance. Do not swap l₁ and l₂.

Ohm's law, Kirchhoff's laws, Wheatstone bridge, potentiometer — Maharashtra HSC Physics Ch 9

📐 13 formulas✏️ 3 examples🎯 5 practice⚖️ 5 marks🏫 Maharashtra State Board📚 Class 12✓ 2025–26 syllabus

💡

Board Exam Tips

→Kirchhoff's laws — statement, sign convention and application to a two-loop circuit — is a very common 4-mark HSC question. Learn the sign convention: EMF rise = +, drop = −.
→Derivation of the balanced Wheatstone bridge condition (P/Q = R/S) is asked almost every alternate year. Draw the network clearly with all four resistances labelled.
→Potentiometer questions frequently ask for comparison of EMFs of two cells (E₁/E₂ = l₁/l₂). Learn the working principle and the sensitivity condition.
→For a real cell: V = ε − Ir. Do not confuse EMF (ε) with terminal potential (V). Board deducts marks for using them interchangeably.
→Always mention units (Ω, V, A, Ω·m) after every numerical answer. Missing units = 1 mark lost per numerical.

📐 Formulas(13)

Ohm's Law★ Board fav

V = I R

Resistivity

R = ρ \frac{l}{A}

Symbol	Meaning
$ρ$	Resistivity (Ω·m)
$l$	Length of conductor (m)
$A$	Area of cross-section (m²)

Drift Velocity and Current★ Board fav

I = n A e v_{d}

Mobility

μ = \frac{v _{d}}{E}

Conductivity from Mobility

σ = n e μ

Temperature Dependence of Resistance

R_{T} = R_{0} [1 + α (T - T_{0})]

Kirchhoff's Current Law (KCL)★ Board fav

\sum_{j u n c t i o n} I = 0

Kirchhoff's Voltage Law (KVL)★ Board fav

\sum_{l oo p} Δ V = 0

Wheatstone Bridge — Balanced Condition★ Board fav

\frac{P}{Q} = \frac{R}{S}

Potentiometer Principle★ Board fav

ε \propto l \Rightarrow \frac{ε _{1}}{ε _{2}} = \frac{l _{1}}{l _{2}}

Internal Resistance from Potentiometer

r = R (\frac{l _{1} - l _{2}}{l _{2}})

Cells in Series and Parallel

ε_{e q}^{ser i es} = ε_{1} + ε_{2}, \frac{1}{r _{e q}^{p a r a l l e l}} = \frac{1}{r _{1}} + \frac{1}{r _{2}}

Power Dissipated

P = V I = I^{2} R = \frac{V ^{2}}{R}

✏️ Solved Examples

1Solved Exampleeasy3 steps

A wire of length 2 m and cross-section 0.5 mm² has resistance 10 Ω. Find its resistivity.

Note given data in SI units.

l = 2 m, A = 0.5 \times 1 0^{- 6} m^{2}, R = 10 Ω

2Solved Exampleboard3 steps

In a Wheatstone bridge, P = 4 Ω, Q = 8 Ω, R = 6 Ω. Find the value of S for balance.

At balance P/Q = R/S.

\frac{P}{Q} = \frac{R}{S}

3Solved ExampleHOTS4 steps

Two cells of EMF 2 V and 4 V and internal resistances 1 Ω and 2 Ω are joined in parallel to feed an external resistance of 10 Ω. Find the current through the 10 Ω resistor.

Equivalent EMF for cells in parallel:

ε_{e q} = \frac{ε _{1} / r _{1} + ε _{2} / r _{2}}{1/ r _{1} + 1/ r _{2}}

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Confusing EMF (ε) with terminal potential difference (V)
✓V = ε − Ir. When current flows, V < ε; only in open circuit V = ε.
2
Using KVL without a consistent sign convention
✓Fix a direction of traversal. EMF rise = +, EMF drop = −; resistor drop in direction of current = −.
3
Assuming Wheatstone bridge is balanced whenever galvanometer shows a small current
✓Balance means EXACTLY zero galvanometer current. Otherwise not balanced.
4
Applying ρ = R·A/l with A in mm² and l in cm
✓Convert all to SI: metres and m². Otherwise ρ is off by many orders of magnitude.
5
Assuming drift velocity is close to electron thermal speed
✓v_d is typically 10⁻⁴ m/s — very small. Thermal speed is 10⁶ m/s. Do not confuse.
6
Forgetting factor of internal resistance in potentiometer internal-resistance formula
✓Use r = R[(l₁ − l₂)/l₂] where R is the shunt resistance. Do not swap l₁ and l₂.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
A copper wire has n = 8.5×10²⁸ /m³. Find the drift velocity for a current of 3 A through a wire of cross-section 2×10⁻⁶ m².
Q2
A cell of EMF 2 V and internal resistance 0.5 Ω is connected to an external 4.5 Ω resistor. Find the terminal voltage.
Q3
Two resistors 6 Ω and 3 Ω are connected in parallel across a 6 V battery of negligible internal resistance. Find the current from the battery.
Q4
In a potentiometer, cell of EMF 1.5 V balances at 60 cm. Another cell balances at 80 cm on the same potentiometer. Find the EMF of the second cell.
Q5
State Kirchhoff's laws and use them to derive the balanced Wheatstone bridge condition.

📝 Notes

Current Electricity — Maharashtra HSC Overview

Chapter 9 of the Maharashtra Board Class 12 Physics textbook covers the microscopic origin of current, Ohm's law, Kirchhoff's laws, Wheatstone bridge and the potentiometer.

What the Maharashtra syllabus emphasises

Formal statement and sign convention of Kirchhoff's laws — the Balbharati textbook devotes an entire section to this and expects students to state, prove and apply both KCL and KVL. CBSE (NCERT) is comparatively brief.
Full derivation of the balanced Wheatstone bridge using Kirchhoff's laws — Maharashtra board favours this over the shortcut version.
Potentiometer applications — comparing EMFs of two cells, and determining internal resistance of a cell — are Maharashtra-specific 3-mark favourites.
Cells in mixed grouping (both series and parallel combined) appears more often in Maharashtra numericals than in CBSE.

Approach tips

Always draw a schematic circuit and label currents I₁, I₂, I₃ with directions before applying KVL/KCL.
The potentiometer is a null method — no current is drawn from the cell being measured, so it gives the true EMF. Mention this in theory answers.
Remember: R depends on temperature; ρ is more fundamental. Semiconductors have negative α — the Balbharati textbook mentions this specifically.