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# Fundamentals of Physics Chapter 27 Solutions: Circuits

Halliday Resnick & Walker Volume 2 Solutions Chapter 27 ‘Circuits’ can indeed be of great assistance if you ever come across some doubts and queries regarding this chapter. This chapter will give you an insight into various types of circuits such as single-loop circuits, multi-loop circuits, an ammeter & voltmeter, and RC circuits. These concepts will display a clear picture in front of you about all the facts regarding circuits. You will understand about the loop rule, resistance rule, and emf rule. Also, you will be able to learn about internal resistance, how to find potential difference between two points in a circuit, grounding circuits, capacitors, capacitive time constant and many more.

Resnick Halliday Physics solutions and Walker Volume 2 Circuits Solutions contain one exercise that has 4 modules and around 105 questions in total. All such questions coherently cover the major topics of the chapter like single loop circuits, multi-loop circuits, an ammeter, and voltmeter, etc. These questions are organized as per the latest syllabus of Physics for competitive exams like IIT JEE and NEET. All you need to do is, have the proper practice of these questions if you are willing to outshine in your exams.

Instasolv provides you with the solutions of Resnick Halliday and Walker Volume 2 Circuits in a stepwise manner. You will find ease while solving the problems of any type related to this chapter once you refer to our explanatory solutions. This could also be a better option if you are an aspirant of some prestigious examinations like JEE and NEET and are preparing for Class 12 board exams along with it.

## Important Topics of Resnick Halliday & Walker Fundamental of Physics Volume 2 Solutions Chapter 27: Circuits

•   EMF-

Electromotive force or (Emf) is nothing, it is actually the energy provided by a cell per coulomb of charge passing through it.

In other words, it is an output when the energy is imparted by an energy source. Sources like generators and motors doing work on the electric charges produce emf. It is measured in volts and given by:

Emf = dw / dq

•     Loop Rule-

The algebraic sum of all the potential differences in any loop must be equal to zero.

∑ (change in potential differences) = 0

•     Junction Rule-

The algebraic sum of all the currents entering the section must be equal to the sum of all the currents leaving the section.

• Single-Loop Circuits-

Single- loop circuits are those types of circuits where all the elements are connected in a way that makes a one circuit-loop, and they are also connected with almost two elements of the other circuits. Here’s an example:

For single-loop circuits containing ε,  is the emf, r is the internal resistance, and resistance R, respectively. Current must be equal to –

I  =    ε /  R + r

Series- Resistances-

When resistances are connected in series, then the current with a similar magnitude will flow across it. The equivalent resistance of the combination of resistances is-

Rtot = R1 + R2 + R3 + …………...+ Rn

•     Parallel Resistances-

When the resistances are connected parallelly across the circuit. They will possess the same potential difference. The equivalent resistance of the combination of resistances is-

1/Req = 1/R1 + 1/R2 + 1/R3 …………..1 /Rn

•     RC Circuits-

RC Circuits is a resistor-capacitor circuit. These circuits are driven by an emf (V)  or a current source. The simplest RC Circuit contains only one resistor and one capacitor. The RC circuit is given below-

The simplest RC Circuit we know is resistance and capacitor in parallel. When a circuit possesses only one resistance and capacitor. In this situation, the capacitor in the circuit will discharge its stored energy through the resistance. The voltage in this condition will be determined using Kirchhoff’s current law.

Consider this linear differential equation-

After solving this equation you will find-

Here, we can see that the voltage across the circuit is time-dependent.

Where Vo is a voltage at time t=0

The time required to reach the voltage Vo  / e is RC time constant.

Where R, is resistance measured in ohms and C, is a capacitor in farads.

### Exercise Discussion of Halliday Resnick & Walker Fundamental of Physics Volume 2 Solutions Chapter 27 Circuits

Module 1: Single-Loop Circuits

Module-27.1 is about the single-loop circuits and has 17 odd questions. These questions use the concepts involving single-loop circuits. You should know how to apply the loop rule, resistance rule, and having a little bit of knowledge on real batteries will help you in solving such questions.

Module 2: Multiloop Circuits

In the module-27.2, there are 31 questions in total. These questions are from multi-loop circuits. In some of the questions, you need to find the potential difference between two points, equivalent resistance, and currents, etc. Practising these questions, you will be able to understand all things about multi-loop circuits.

Module 3: The Ammeter and the Voltmeter

Module-27.3 contains 8 questions, and they are using the concepts of an ammeter & voltmeter. In questions, you have to determine the current in the ammeter and voltmeter, and also some questions, on changing terms in ammeter and voltmeter what is the resistance or current in the circuit.

Module 4: RC Circuits

Module-27.4 has 13 questions at which you need to brush up your knowledge of the inner concepts of RC circuits. You will encounter the various types of questions in this module i.e. some of them you need to compute the time constant, find the capacitance, resistance, etc.