Category: HC Verma Part 2: Electricity

Problem Statement Solve the capacitor/capacitance problem: $C_1 = 4\mu$F charged to 200 V and $C_2 = 6\mu$F charged to 100 V are connected in parallel but with opposite polarity (positive plate of one to negative of other). Find the common voltage and heat released. Net charge = $Q_1 – Q_2$ (opposite polarity) Step 1: $Q_1…

Problem Statement Solve the capacitor/capacitance problem: $C_1 = 5\mu$F is charged to 80 V. $C_2 = 3\mu$F is charged to 40 V (same polarity). They are then connected in parallel (positive to positive). Find the common voltage. Total charge conserved: $Q_{total} = Q_1 + Q_2$ Step 1: $Q_1 = 5\times80 = 400\,\mu$C, $Q_2 = 3\times40…

Problem Statement Solve the capacitor/capacitance problem: An infinite ladder network of capacitors has alternating $C$ in series and $C$ in parallel. Find the effective capacitance between the input terminals. Self-similarity: the network repeats itself; let effective capacitance $= X$ Step 1: The infinite ladder is self-similar. Effective capacitance $X$ Given Information Plate area $A$ (for…

Problem Statement Analyze the circuit: A capacitor $C$ is charged from a battery of EMF $V$ through a resistor. Find (a) energy supplied by battery, (b) energy stored in capacitor, and (c) energy dissipated in resistor. Battery supplies $QV = CV^2$; capacitor stores $\frac{1}{2}CV^2$; rest is heat (a) Charge delivered: $Q = CV$. Energy f…

Problem Statement A parallel plate capacitor has plate separation 2 mm and dielectric constant 3. The breakdown field of the dielectric is $3\times10^7$ V/m. Find the maximum voltage that can be applied. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts &…

Problem Statement Solve the capacitor/capacitance problem: A capacitor $C = 10\mu$F in series with resistance $R = 100\,\Omega$ is connected to a 12 V battery. Find the initial current and the final charge on the capacitor. Initially capacitor acts as wire: $I_0 = V/R$ Finally capacitor fully charged: $Q_f = CV$ Step 1: Initial current:…

Problem Statement Solve the capacitor/capacitance problem: A parallel plate capacitor has plate area $A = 10$ cm$^2$ and charge density $\sigma = 1\mu$C/m$^2$. Find the electrostatic force between the plates. $F = \sigma^2 A/(2\varepsilon_0)$ Step 1: $\sigma = 10^{-6}$ C/m$^2$, $A = 10^{-3}$ m$^2$. Step 2: $$F = \frac{\sigma^2 A}{2\varepsilon_0} = \frac{(10 Given Information Plate…

Problem Statement Solve the capacitor/capacitance problem: A parallel plate capacitor ($C = 5\mu$F) is charged to 100 V and then disconnected. The plate separation is then doubled. Find the new capacitance, voltage, and energy. Charge conserved; $C$ halves when $d$ doubles; $V = Q/C$ doubles; $U = Q^2/(2C)$ doubles Step 1: $Q = 5\times10^{-6}\times100 =…

Problem Statement Solve the capacitor/capacitance problem: Capacitors of $1\mu$F, $2\mu$F, $3\mu$F are in a network where $C_1$ and $C_2$ are in series, and $C_3$ is in parallel with the series combination, all connected to 6 V. Find the charge on each. Series-parallel reduction Step 1: $C_{12}$ (series) $= \dfrac{1\times2}{1+2} = \dfrac{2}{3}\,\mu$F. Step Given Information Plate…

Problem Statement Solve the capacitor/capacitance problem: Five capacitors, each of $2\mu$F, are connected in a Wheatstone bridge configuration. Find the equivalent capacitance between the battery terminals if the bridge is balanced. Balanced Wheatstone bridge: no charge on the middle capacitor Two pairs in series, then parallel Step 1: When balanced, the m Given Information Plate…