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Soumya Sir's Physics Class
GOLDEN NUMERICALS
Class 12 High-Probability Problems
1. The "Circuit Breaker"
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"Calculate currents $I_1, I_2, I_3$ in the loops..."
The Trap: Wrong sign convention destroys the whole answer.
Step 1: Mark Loops (Clockwise).
Step 2: Apply KVL ($\sum \Delta V = 0$).
Current with Loop $\to$ -IR
Current against Loop $\to$ +IR
Step 1: Mark Loops (Clockwise).
Step 2: Apply KVL ($\sum \Delta V = 0$).
Current with Loop $\to$ -IR
Current against Loop $\to$ +IR
2. The "Impedance Triangle"
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"Find the power factor and current in Series LCR..."
Step 1: Find Reactances ($X_L = \omega L$, $X_C = 1/\omega C$).
Step 2: Find Impedance ($Z$).
$Z = \sqrt{R^2 + (X_L - X_C)^2}$
Step 3: Current $I_{rms} = V_{rms} / Z$.
Step 2: Find Impedance ($Z$).
$Z = \sqrt{R^2 + (X_L - X_C)^2}$
Step 3: Current $I_{rms} = V_{rms} / Z$.
3. The "Fringe Counter"
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"Light of wavelength 500nm used. Find fringe width..."
The Trap: Units! $d$ is usually in mm, $\lambda$ in nm.
Formula:
$\beta = \frac{\lambda D}{d}$
For nth Bright Fringe: $y_n = n \beta$
Formula:
$\beta = \frac{\lambda D}{d}$
For nth Bright Fringe: $y_n = n \beta$
4. The "Lens Combo"
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"A convex lens (f=20) is in contact with concave (f=10)..."
Sign Convention: Convex (+f), Concave (-f).
Step 1: Power Additive.
$P_{net} = P_1 + P_2$
Step 2: Focal Length.
$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$
Step 1: Power Additive.
$P_{net} = P_1 + P_2$
Step 2: Focal Length.
$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$
5. Einstein's Equation
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"Work function is 2.14 eV. Find Kinetic Energy..."
The Trap: Do not mix eV and Joules!
Formula:
$h\nu = \phi_0 + K_{max}$
Tip: Convert all to eV first. ($E = 12400 / \lambda(\text{\AA})$ eV).
Formula:
$h\nu = \phi_0 + K_{max}$
Tip: Convert all to eV first. ($E = 12400 / \lambda(\text{\AA})$ eV).
6. The "Energy Jump"
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"Electron jumps from n=3 to n=2..."
Step 1: Find Energy Difference ($\Delta E$).
$E_n = \frac{-13.6}{n^2} \text{ eV}$
Step 2: Find Wavelength.
$\lambda = \frac{12400}{\Delta E(\text{eV})} \text{ \AA}$
$E_n = \frac{-13.6}{n^2} \text{ eV}$
Step 2: Find Wavelength.
$\lambda = \frac{12400}{\Delta E(\text{eV})} \text{ \AA}$
7. Galvanometer Conversion
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Case A: To Ammeter (Parallel Shunt)
Logic: Current divides. Most goes through Shunt.
$S = \frac{I_g G}{I - I_g}$
Case B: To Voltmeter (Series Resistance)
Logic: Voltage divides. Total R increases.
$R = \frac{V}{I_g} - G$
Logic: Current divides. Most goes through Shunt.
$S = \frac{I_g G}{I - I_g}$
Case B: To Voltmeter (Series Resistance)
Logic: Voltage divides. Total R increases.
$R = \frac{V}{I_g} - G$
⚠️ CRITICAL UNIT CONVERSIONS
1 eV = $1.6 \times 10^{-19}$ J
1 \AA = $10^{-10}$ m
1 $\mu$C = $10^{-6}$ C
1 nm = $10^{-9}$ m
1 eV = $1.6 \times 10^{-19}$ J
1 \AA = $10^{-10}$ m
1 $\mu$C = $10^{-6}$ C
1 nm = $10^{-9}$ m
