*In this tutorial, we will deal with more problems involving resistors and capacitors. We introduce the idea of Composite dielectrics as well. *
*Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE Main or Advanced/AIEEE, and anyone else who needs this Tutorial as a reference!*
**Here are a few of the problems you will learn how to solve in this tutorial :**
**Q: **alculate the time constant of a given circuit. What value will be the voltage across the capacitor at various points of time? Calculate the time taken by the capacitor to get fully charged?
**Q: **Calculate the time constant of a given RC discharging circuit.
**Q: **A 0.5 MΩ resistor is connected in series with 8µF capacitor with a supply of 200v DC supply. Calculate, Initial charging current, time taken for the capacitor to charge up to 160v, current and voltage across capacitor 4 s after it is connected to the supply.
**Q:** A 50 F capacitor is charged to 200v and connected parallel to an uncharged capacitor of 30 F. Find voltage across the capacitors , electrostatic energies before and after the connection is made.
**Q: **Find the charge and the current for t > 0 in a series RC circuit where R = 10 W, C = 4 × 10-3 F and E = 85 cos 150t V. Assume that when the switch is closed at t = 0, the charge on the capacitor is -0.05 C.
**Q: **A series RC circuit with R = 5 W and C = 0.02 F is connected with a battery of E = 100 V. At t = 0, the voltage across the capacitor is zero.
**Q: **A 20 uF capacitor is connected in series with a 50 kresistor and the circuit is connected to a 20 V, d.c. supply. Determine
(a) the initial value of the current ﬂowing, (b) the time constant of the circuit, (c) the value of the current one second after connection, (d) the value of the capacitor voltage two seconds after connection, and (e) the time after connection when the resistor voltage is 15 V
**Q: **A capacitor is charged to 100 V and then discharged through a 50K resistor. If the time constant of the circuit is 0.8 s, determine: (a) the value of the capacitor, (b) the time for the capacitor voltage to fall to 20 V, (c) the current ﬂowing when the capacitor has been discharging for 0.5 s. (d) the voltage drop across the resistor when the capacitor has been discharging for one second.
**Composite dielectrics:**
An important concept introduced in this tutorial. The dielectric medium between a capacitor can be composite as by combination of two or more dielectrics. In this case the capacitor can be partitioned into different capacitors. Consider a capacitor which has two dielectric medium E1 and E2 with the distance d1 and d2 respectively. It can be partitioned into two different capacitors in series as will be explained in the tutorial.
**Charging and Discharging of a Capacitor**
The rate of charging of the capacitor depends on the product of R and C. This is usually called the time constant and denoted by the Greek letter tau = RC.
**Energy stored in a capacitor**
Energy stored in a capacitor is W = (1/2)CV^{2} It can be deduced starting from the force of attraction between two plates of a capacitor which is given by F.d = (1/2)CV^{2}
**Complete tutorial with solved problems :**
**MCQ Quiz on Basic Circuits with Resistance (Most of these are High School level questions)**
#### MCQ Quiz: Circuits with ResistanceGoogle Spreadsheet Form
**Related Tutorials ( Introduction to Electrical Circuits - DC ) :**
**Circuit Theory 1a - Introduction to Electrical Engineering, DC Circuits, ****Resistance and Capacitance, Kirchoff Law**
| Resistors, Capacitors, problems related to these. | **Circuit Theory 1b - More solved problems related to DC Circuits with Resistance and Capacitance**
| Capacitors, computing capacitance, RC Circuits, time constant of decay, computing voltage and electrostatic energy across a capacitance | **Circuit Theory 2a - Introducing Inductors**
| Inductors, inductance, computing self-inductance, flux-linkages, computing energy stored as a magnetic field in a coil, mutual inductance, dot convention,
| **Circuit Theory 2b - Problems related to RL, LC, RLC circuits**
| Introducing the concept of oscillations. Solving problems related to RL, LC and RLC circuits using calculus based techniques. | **Circuit Theory 3a - Electrical Networks and Network Theorems**
| Different kind of network elements: Active and passive, linear and non-linear, lumped and distributed. Voltage and current sources. Superposition theorem, Thevenin (or Helmholtz) theorem and problems based on these. | **Circuit Theory 3b - More network theorems, solved problems**
| More solved problems and examples related to electrical networks. Star and Delta network transformations, maximum power transfer theorem, Compensation theorem and Tellegen's Theorem and examples related to these. | |