Category: HC Verma Part 2: Electricity

Problem Statement Solve the capacitor/capacitance problem: Find the capacitive reactance of a $20\mu$F capacitor at frequency 50 Hz and at 1 kHz. See problem statement for all given quantities. Capacitors store electric charge on conducting plates separated by an insulator (dielectric). The capacitance $C = Q/V$ depends on geometry and dielectric constant. Given Information Plate…

Problem Statement Solve the capacitor/capacitance problem: A $10\mu$F capacitor is being charged through $50\,\Omega$ from a 20 V source. How long does it take to charge to 90% of the final voltage? See problem statement for all given quantities. Capacitors store electric charge on conducting plates separated by an insulator (dielectric). The capacitance $C Given…

Problem Statement Solve the capacitor/capacitance problem: Three equal capacitors, each $C$, are connected in a delta (triangle) configuration. Find the equivalent capacitance between any two terminals. See problem statement for all given quantities. Capacitors store electric charge on conducting plates separated by an insulator (dielectric). The capacitanc Given Information Plate area $A$ (for parallel plate)…

Problem Statement Solve the capacitor/capacitance problem: A parallel plate capacitor with plate area $A$, separation $d$, is filled with a dielectric that has both dielectric constant $K$ and conductivity $\sigma_c$. A voltage $V_0$ is applied. Find the steady-state charge distribution. See problem statement for all given quantities. Capacitors store elect Given Information Plate area $A$…

Problem Statement Solve the work-energy problem: Three capacitors $2\mu$F, $4\mu$F, and $6\mu$F are connected in series to a 24 V battery. Find the charge and voltage across each. See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the rele Given Information Mass $m$,…

Problem Statement Solve the capacitor/capacitance problem: Find the self-capacitance of the Earth (radius $R_E = 6.4\times10^6$ m). How much charge would give Earth a potential of 1 volt? $C = 4\pi\varepsilon_0 R_E$; $Q = CV$ Step 1: $$C = 4\pi\varepsilon_0 R_E = \frac{R_E}{k} = \frac{6.4\times10^6}{9\times10^9} \approx 7.11\times10^{-4} \text{ F} \approx 7 Given Information Plate area…

Problem Statement Solve the capacitor/capacitance problem: Derive the expression for work done in charging a capacitor $C$ to charge $Q$. $dW = V\,dq = (q/C)dq$ Step 1: At any instant when charge on capacitor is $q$, voltage = $q/C$. Work done to add $dq$ more charge: $$dW = \frac{q}{C}dq$$ Step 2: Total work to charge…

Problem Statement Solve the capacitor/capacitance problem: A parallel plate capacitor has dielectric constant varying as $K(x) = K_0(1 + x/d)$ from one plate to the other (separation $d$, area $A$). Find the capacitance. Treat as infinite series of thin slabs; sum their capacitances as series capacitors: $1/C = \int_0^d dx/(K(x)\varepsilon_0 A)$ Step 1: Eac Given…

Problem Statement Solve the capacitor/capacitance problem: Find the equivalent capacitance between terminals A and B when: $C_1$ (between A and C), $C_2$ (between B and C), $C_3$ (between A and B) are all equal to $C$. $C_3$ is in parallel with ($C_1$ in series with $C_2$) Step 1: $C_1$ and $C_2$ in series: $C_{12} =…

Problem Statement Solve the capacitor/capacitance problem: A $5\mu$F capacitor is charged through $200\,\Omega$ from a 10 V battery. Find the voltage across the capacitor after $1$ ms. $V_C(t) = V_0(1-e^{-t/\tau})$, $\tau = RC$ Step 1: $\tau = RC = 200\times5\times10^{-6} = 10^{-3}$ s $= 1$ ms. Step 2: At $t = \tau = 1$ ms:…