Science Numerical Problem Formulae

10th Science - Quarterly Exam 2025 - Important Numerical Problem Formulae

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10th Science Formula Sheet

ELECTRICITY

Symbols and SI UNIT

Symbol	Quantity	SI Unit Symbol	SI Unit Name
I	Current	A	Ampere
Q	Charge	C	Coulomb
t	Time	s	Second
V	Potential Difference	V	Volt
W	Work	J	Joule
E	Energy	J	Joule
R	Resistance	Ω	Ohm
A	Area	m²	Unit² (meter square)
ρ	Resistivity	Ωm	Ohm.meter

Formulas

1. Current, Charge, and Time

\( I = \frac{Q}{t} \)

\( t = \frac{Q}{I} \)

\( Q = I \cdot t \)

2. Potential Difference, Work, and Charge

\( V = \frac{W}{Q} \)

\( Q = \frac{W}{V} \)

\( W = Q \cdot V \)

3. Ohm's Law

Potential difference is directly proportional to the current: \( V \propto I \)

\( V = I \cdot R \)

\( I = \frac{V}{R} \)

\( R = \frac{V}{I} \)

4. Factors Affecting Resistance

Resistance is directly proportional to length (l) and inversely proportional to the area of cross-section (A).

\( R \propto l \) and \( R \propto \frac{1}{A} \)

\( R = \rho \frac{l}{A} \)

5. Resistors in Series

\( R_s = R_1 + R_2 + R_3 + \dots \)

6. Resistors in Parallel

\( \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots \)

7. Heat (Joule's Law of Heating)

\( H = I^2 R t \)

\( H = \frac{V^2}{R} t \)

\( H = V I t \)

8. Power

Note: Work (W) = Energy (E)

\( P = \frac{W}{t} \)

\( P = I^2 R \)

\( P = V I \)

\( P = \frac{V^2}{R} \)

9. Quantization of Charge

\( Q = n \cdot e \)

Where:
n → no. of electrons
e → charge on one electron (\(1.6 \times 10^{-19} C\))

LIGHT

1. Laws of Reflection

Angle of incidence = Angle of Reflection

\( \angle i = \angle r \)

2. Relation between Radius of Curvature and Focal Length

\( R = 2f \)

\( f = \frac{R}{2} \)

Where:
R = Radius of curvature
f = focal length

3. Mirror Formula

\( \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \)

Where:
v = distance of Image
u = distance of Object

4. Magnification (Mirrors)

\( m = \frac{h_i}{h_o} = \frac{v}{u} \)

Where:
hi = height of Image
ho = height of Object

5. Absolute Refractive Index

\( n = \frac{c}{v} \)

Where:
n = Index
c = velocity of light
v = velocity of light in medium

6. Relative Refractive Index

\( n_{21} = \frac{n_2}{n_1} \)

Also, \( n_{12} = \frac{n_1}{n_2} \)

Where:
n₂ = Speed of light in medium 2
n₁ = Speed of light in medium 1

7. Snell's Law

\( n_1 \sin i = n_2 \sin r \)

\( \Rightarrow \frac{\sin i}{\sin r} = \frac{n_2}{n_1} \)

8. Lens Formula

\( \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \)

9. Magnification (Lenses)

\( m = \frac{h_i}{h_o} = \frac{v}{u} \)

10. Power of a Lens

\( P = \frac{1}{f} \)

Where:
P = Power
f = focal length in meter

11. Power of Combination

\( P = P_1 + P_2 + P_3 + \dots \)

\( \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3} + \dots \)

MAGNETIC EFFECTS

The strength of the magnetic field (B) is related to:

Proportionality	Description
\( B \propto I \)	I = Current
\( B \propto \frac{1}{r} \)	r = Distance from Conductor
\( B \propto N \)	N = No. of turns

Where B = Magnetic field

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