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Contents

1 For EC103, Assignment 2
- 1.1 1A source on:
- 1.2 2A source on:
2 For 620-143 Assignment 2
3 For physics cheat sheet

For EC103, Assignment 2

1A source on:

Node 1: $\frac{v_2 - v_1}{10} + 1A + \frac{2v_x - v_1}{15} = \frac{v_1}{5}$ Leads to $15 v 1 - 7 v 2 = 30$

Node 2: $\frac{2v_2 - 2v_1 - v_2}{10} = \frac{v_2 - v_1}{10} + \frac{2v_2}{10}$ Leads to $v 1 + 2 v 2 = 0$

2A source on:

Node 1: $\frac{v_2 - v_1}{10} + \frac{2v_2 - 2v_1 - v_1}{15} = \frac{v_1}{5}$ Leads to $7 v 2 - 15 v 1 = 0$

Node 2: $\frac{2v_2 - 2v_1 - v_2}{10} + 2A = \frac{2v_2}{10} + \frac{v_2 - v_1}{10}$ Leads to $2 v 2 + v 1 = 20 A$

For 620-143 Assignment 2

$B(m) = \int_{0}^{1} x^{m-1} (1-x)^{\frac{-1}{2}} dx$

For physics cheat sheet

Movement

Average velocity: $v_{average} = \frac{s}{t}$

Acceleration: $a = \frac{ \Delta\ v}{t} = \frac{v-u}{t}$

Force due to gravity: $F g = m g$

Momentum: $p = m v$

Impulse: $F \Delta\ t = m \Delta\ v$

Work: $W = Fs = \Delta\ Energy$

Kinetic energy: $K_e = \frac{1}{2}mv^2$

Gravitational potential energy: $G P e = m g h$

Force from a spring: $F = - k x$

Elastic potential energy: $EP_e = \frac{1}{2}kx^2$

Velocity around a circle: $v =\frac{2 \pi\ r}{T}$

Acceleration around a circle: $a = \frac{v^2}{r} = \frac{4 \pi\ ^2r}{T^2}$

Centripetal force: $F_c = \frac{mv^2}{r}$

Universal gravitation: (F is in $N K g - 1$ ) $F = G\frac{M_1M_2}{r^2}$

Gravitational field strength: $F = G\frac{M}{r^2}$

Orbits around the same mass: $\frac{T_1^2}{T_2^2} = \frac{r_1^3}{r_2^3}$

Electronics

Work: $W = V q = V I t$

Power: $P = VI = I^2R = \frac{V^2}{R}$

Voltage: $V = I R$

Votage divider: $V_{out} = V_{in} \frac{R_2}{R_1 + R_2}$

Voltage gain: $G = \frac{ \Delta\ V_{out}}{ \Delta\ V_{in}}$

Further Electronics

RMS: $V_{RMS} = \frac{V_{peak}}{\sqrt{2}}$

$I_{RMS} = \frac{I_{peak}}{\sqrt{2}}$

Transformer: $\frac{N_p}{N_s} = \frac{V_p}{V_s} = \frac{I_s}{I_p}$

$P i n = P o u t$

Time constant: $t = R C$

Ripple voltage: $V_{R(p-p)} = V_{max} - V_{min} = \frac{V_{max}T}{RC}$

Light

Path difference for nodal lines: $p.d. = (n - \frac{1}{2}) \lambda\$

Path difference for antinodal lines: $p.d. = n \lambda\$

For the double slit experiment: $w = \frac{ \lambda\ L}{d} = \frac{vL}{ \mathit{f} d}$

For single slit experiment: $sin \Theta\ = \frac{ \lambda\ }{w}$

Energy of a photon: $E = h \mathit{f} = \frac{hc}{ \lambda\ }$

Number of photos emitted by a light source: $E l i g h t s o u r c e = n E p h o t o n$

The photoelectric effect: $h f = W + K E e l e c t r o n$

Photon Momentum: $p = \frac{E}{c} = \frac{h \mathit{f}}{c} = \frac{ \mathit{f}}{ \lambda}$

de Broglie Wavelength: $\mathbf{de\ Broglie\ wavelength}\ \lambda\ = \frac{h}{p} = \frac{h}{mv}$

Spectra of atoms: $2 \pi\ r = n \lambda\$

$\varepsilon\ = \frac{-N \Delta\ \phi\ }{ \Delta\ t}$

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