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NEB Class 12 Physics Electrical Circuit one Note Handwritten in PDF
Kirchhoff’s Laws Foundation of Circuit Analysis
Kirchhoff’s Current Law (KCL) First Law: The algebraic sum of all currents at any junction (node) is zero.
Ξ£I = 0 at any node
Physical basis: Conservation of charge charge cannot accumulate at a node.
Convention: Currents flowing INTO junction = positive; flowing OUT = negative
Kirchhoff’s Voltage Law (KVL) Second Law: The algebraic sum of all EMFs equals the algebraic sum of all IR drops around any closed loop.
Ξ£EMF = Ξ£IR around any closed loop
Physical basis: Conservation of energy total voltage gained = total voltage lost in a complete loop.
Procedure for solving with Kirchhoff’s laws:
- Assign current directions (assume directions, negative answer means opposite)
- Apply KCL at each junction
- Apply KVL around independent loops
- Solve simultaneous equations
Wheatstone Bridge Balance Condition
A Wheatstone bridge has four resistors P, Q, R, S arranged in a diamond with a galvanometer between middle nodes.
Balance condition (null deflection in galvanometer): P/Q = R/S (equivalently: PS = QR)
Derivation using KCL and KVL: At balance, no current through galvanometer. Using KVL: IβP = IβR and IβQ = IβS Dividing: P/Q = R/S
Applications:
- Measure unknown resistance accurately
- Basis of Meter Bridge
- Used in sensor circuits (thermistor, strain gauge bridges)
Meter Bridge
A meter bridge is a practical form of Wheatstone bridge using a 100 cm wire.
Working: Balance the bridge by sliding contact D to position where galvanometer reads zero.
Formula: R/X = lβ/(100 β lβ)
Where X = unknown resistance, lβ = balancing length from left end, R = known resistance.
This gives a very accurate measurement because the wire has uniform resistance per unit length.
Potentiometer Principle and Applications
Principle: When no current flows through the cell being measured, the EMF exactly equals the potential drop across the corresponding length of wire.
E = Οl (Ο = potential drop per unit length, l = balancing length)
Advantage over voltmeter: A voltmeter draws current, causing error. A potentiometer works at null (zero current) no current through cell β no error from internal resistance β measures true EMF.
Application 1 Comparing EMFs: Eβ/Eβ = lβ/lβ
Connect each cell in turn, find balancing lengths lβ and lβ. Ratio gives EMF ratio directly.
Application 2 Internal resistance of cell:
- Find balancing length lβ with cell in open circuit (switch open)
- Find balancing length lβ with external resistance R connected (switch closed)
- r = R(lβ β lβ)/lβ
Superconductors and Perfect Conductors
Superconductors:
- Below a critical temperature T_c, resistance drops to exactly zero
- Meissner effect: magnetic fields are completely expelled from inside the superconductor
- Examples: Mercury (T_c = 4.2 K), Niobium, high-temperature superconductors (above 77 K)
- Applications: MRI magnets, maglev trains, particle accelerators, quantum computers
Perfect conductors (Ο = 0):
- A theoretical concept with zero resistivity but no Meissner effect
- Superconductors are NOT just perfect conductors the Meissner effect is the key distinction
Converting Galvanometer
Galvanometer to Ammeter (shunt S in parallel):
- Shunt diverts excess current
- S = I_g Γ G / (I β I_g)
- I_g = galvanometer full scale current, G = galvanometer resistance, I = max circuit current
- Ammeter has very low total resistance
Galvanometer to Voltmeter (series resistance R in series):
- Series R drops excess voltage
- R = (V/I_g) β G
- V = max voltage to measure
- Voltmeter has very high total resistance
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Frequently Asked Questions
What is Kirchhoff’s law in Class 12 Physics?
KCL (first law): sum of all currents at any junction equals zero based on conservation of charge. KVL (second law): sum of all EMFs equals sum of all IR drops around any closed loop based on conservation of energy. Both laws together can solve any complex electrical circuit systematically.
What is the balance condition of Wheatstone bridge?
Wheatstone bridge is balanced (no galvanometer current) when P/Q = R/S. Derived using Kirchhoff’s laws at balance no current flows through galvanometer branch. In meter bridge: R/X = lβ/(100βlβ) where lβ is balancing length. Used to accurately measure unknown resistance without disturbing the circuit.
What is the advantage of potentiometer over voltmeter?
Voltmeter draws current from circuit causing voltage drop error due to internal resistance. Potentiometer works at null condition no current flows through the cell being measured so no error from internal resistance. Potentiometer measures true EMF accurately. This is a frequently asked 2-mark conceptual question in NEB exams.
How does potentiometer compare EMFs of two cells?
Connect each cell in turn and find balancing length where galvanometer reads zero. Eβ/Eβ = lβ/lβ. At balancing length no current flows through the cell so its internal resistance causes no error. This gives accurate ratio of EMFs. The method works because potential drop per unit length of wire is uniform throughout.
How to find internal resistance using potentiometer Class 12?
Find balancing length lβ with cell in open circuit (switch open). Find balancing length lβ with external resistance R connected (switch closed). Internal resistance r = R(lββlβ)/lβ. This method is accurate because potentiometer draws no current from cell during measurement unlike ammeter-voltmeter method.
What is the difference between superconductor and perfect conductor?
Superconductor: resistance drops to exactly zero below critical temperature AND shows Meissner effect (expels magnetic field completely from interior). Perfect conductor: zero resistivity theoretically but no Meissner effect. Superconductors are not simply perfect conductors the Meissner effect is the fundamental distinguishing property.
How to convert galvanometer to ammeter and voltmeter?
Ammeter: connect low resistance shunt S in parallel S = IgG/(IβIg). Shunt diverts excess current. Ammeter has very low resistance. Voltmeter: connect high resistance R in series R = V/Ig β G. Series resistance drops excess voltage. Voltmeter has very high resistance. These conversions are standard 2-mark NEB questions.
Which electrical circuits topics are most important for Exam?
Most important: Kirchhoff’s law application to circuits (4 marks), Wheatstone bridge balance condition derivation (4 marks), potentiometer EMF comparison and internal resistance (4 marks each), galvanometer conversion (2 marks). Potentiometer and Wheatstone bridge questions appear in every NEB board examination paper.
