Author Capstone Axis

⚡ Electric Current – Quick & Clear Notes 1. Charges on the Move 😊 An electric current appears whenever charges flow. Lightning is a dramatic natural current, while the gentle glow of a torch shows a steady, tame current we use every day. :contentReference[oaicite:0]{index=0} 2. Defining Current Imagine a small area placed ⟂ (perpendicular) to […]

3.3 Electric Currents in Conductors 💡 1. Electric Current: the basic idea Current tells us “how much charge zooms past every second.” The average (steady) value is \( I = \dfrac{Q}{t} \) :contentReference[oaicite:0]{index=0} and the instantaneous value is the limit form \( I(t)=\displaystyle\lim_{\Delta t\to 0}\dfrac{\Delta Q}{\Delta t}\). :contentReference[oaicite:1]{index=1} Unit: ampere (A). Domestic gadgets draw a few

Ohm’s Law 🚀 Georg Simon Ohm found in 1828 that the potential difference V across a conductor is directly proportional to the current I flowing through it: \(V \propto I \Rightarrow V = R\,I\) — where R is the resistance measured in ohms (Ω). :contentReference[oaicite:0]{index=0} What resistance really means 😎 Resistance depends on size: doubling

Energy Stored in a Capacitor 🔋 Move charge from one plate to the other and you do work. That work parks itself as electrostatic potential energy inside the capacitor.:contentReference[oaicite:0]{index=0} 1. Charging Up Step-by-Step 🏗️ Mid-way through charging, the positive plate holds charge \(Q’\) while the negative plate holds \(-Q’\). The potential difference sits at \(V’

Effect of Dielectric on Capacitance 🔌 1. Quick recap: bare capacitor For two large parallel plates (area \(A\)) separated by a gap \(d\) and holding charges \(\pm Q\): Surface charge density: \(\sigma = Q/A\). Uniform electric field between the plates: \(E_0 = \sigma/\varepsilon_0\). :contentReference[oaicite:0]{index=0} Potential difference: \(V_0 = E_0 d\). :contentReference[oaicite:1]{index=1} Capacitance: \(C_0 = \dfrac{\varepsilon_0

Combination of Capacitors 🤝 Putting capacitors together lets us “tune” the total capacitance of a circuit. Two super-useful ways to hook them up are series and parallel. Let’s see how each one works. 🧐 1 · Capacitors in Series 🔗 The same charge \(Q\) flows through every capacitor because any surplus would push charges until balance returns.

🌟 The Parallel-Plate Capacitor A parallel-plate capacitor is the simplest “charge-storage” device we can build: two wide, flat conducting plates of area A held d metres apart. One plate carries charge +Q, the other –Q. Because the gap is tiny compared with plate size (d2 ≪ A), the system acts almost like two infinite sheets

Capacitors & Capacitance 🔋✨ 1. What’s a Capacitor? A capacitor is simply two conductors separated by an insulator. The plates hold charges \( +Q \) and \( -Q \) so the net charge of the whole device stays zero :contentReference[oaicite:0]{index=0}. 2. Charge–Voltage Link The electric field between the plates scales with the stored charge. Push

Electrostatics of Conductors 🪙⚡ Why Metals Act Differently Metals contain mobile electrons that zip around like a gas, colliding with ions inside the lattice. These electrons drift opposite to an applied field but cannot escape the metal :contentReference[oaicite:0]{index=0}. In electrolytes the carriers are ions, yet the principles below stay the same for every solid metallic

Dielectrics & Polarisation ⚡ 1. What are dielectrics? Dielectrics are non-conducting materials with practically no free charge carriers. When an external electric field is applied, they cannot neutralise the field the way conductors do. Instead, the field stretches or re-orients their molecules so that surface charges are induced, creating an opposing field that reduces (but