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Soumya Sir's Physics Class
THE GOLDEN NUMERICALS
Top 7 Guaranteed Exam Question Types
1. The "Bill Calculator"
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"Calculate the cost of running a 2kW heater for 5 hours daily for September..."
The Trap: Time is given in minutes or hours daily.
Step 1: Find Total Energy ($E$) in kWh.
$E = P(\text{kW}) \times t(\text{hours})$
Step 2: Multiply by days (e.g., Sep = 30 days).
Step 3: Cost = Total Unit $\times$ Rate.
Step 1: Find Total Energy ($E$) in kWh.
$E = P(\text{kW}) \times t(\text{hours})$
Step 2: Multiply by days (e.g., Sep = 30 days).
Step 3: Cost = Total Unit $\times$ Rate.
2. The "Circuit Puzzle"
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"Find the reading of the Ammeter in the given circuit..."
The Trick: You cannot find individual Current ($I$) without Total Resistance ($R_{eq}$).
Step 1: Solve Parallel parts first ($R_p = \frac{R_1 R_2}{R_1+R_2}$)
Step 2: Add Series parts ($R_{total} = R_p + R_s$)
Step 3: Use Ohm's Law: $I_{total} = \frac{V_{battery}}{R_{total}}$
Step 1: Solve Parallel parts first ($R_p = \frac{R_1 R_2}{R_1+R_2}$)
Step 2: Add Series parts ($R_{total} = R_p + R_s$)
Step 3: Use Ohm's Law: $I_{total} = \frac{V_{battery}}{R_{total}}$
3. Bulb Rating (V-I-P)
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"A bulb is rated 100W-220V. What is its power when connected to 110V?"
The Concept: Voltage changes, Power changes, but Resistance remains constant.
Step 1: Find R from rating: $R = \frac{V^2}{P}$
Step 2: Use this R for new voltage: $P_{new} = \frac{V_{new}^2}{R}$
Step 1: Find R from rating: $R = \frac{V^2}{P}$
Step 2: Use this R for new voltage: $P_{new} = \frac{V_{new}^2}{R}$
4. Mirror/Lens Position
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"An object is placed 20cm from a concave mirror..."
Sign Convention Check:
$u = -20$ (Always negative!)
$f = -ve$ (Concave) / $+ve$ (Convex)
Formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ (Mirror)
Result: If $v$ is minus (-), it's Real. If plus (+), it's Virtual.
$u = -20$ (Always negative!)
$f = -ve$ (Concave) / $+ve$ (Convex)
Formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ (Mirror)
Result: If $v$ is minus (-), it's Real. If plus (+), it's Virtual.
5. Speed of Light
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"Refractive index of glass is 1.5. Find speed of light in glass."
Formula: $n_m = \frac{c}{v}$
Given: $c = 3 \times 10^8$ m/s (Memorize this!)
Calculation: $v = \frac{3 \times 10^8}{1.5} = 2 \times 10^8$ m/s.
Given: $c = 3 \times 10^8$ m/s (Memorize this!)
Calculation: $v = \frac{3 \times 10^8}{1.5} = 2 \times 10^8$ m/s.
6. Combination Power
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"Two lenses of power +2D and -0.5D are placed in contact..."
Step 1: Add algebraically: $P = P_1 + P_2$
$P = (+2) + (-0.5) = +1.5D$
Step 2: Find Focal Length: $f = \frac{1}{P}$ meters.
(Don't forget to convert to cm if asked: $f = \frac{100}{P}$ cm).
$P = (+2) + (-0.5) = +1.5D$
Step 2: Find Focal Length: $f = \frac{1}{P}$ meters.
(Don't forget to convert to cm if asked: $f = \frac{100}{P}$ cm).
7. The "Spectacle" Problem (Defects of Vision)
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Case A: Myopia (Cannot see Far)
Logic: The Far Point is given ($x$). We need the lens to take object at $\infty$ and show it at $x$.
Formula: $u = \infty$, $v = -x$ (Far point).
Shortcut: $f = -x$ (Focal length = Negative of Far point).
Formula: $u = \infty$, $v = -x$ (Far point).
Shortcut: $f = -x$ (Focal length = Negative of Far point).
Case B: Hypermetropia (Cannot see Near)
Logic: Near point is given ($d'$). Normal near point is $D=25$cm.
Formula: $u = -25$, $v = -d'$ (Given distance).
Use Lens Formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Formula: $u = -25$, $v = -d'$ (Given distance).
Use Lens Formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
