The dead battery of your car provides a potential difference of 9.950 V and has an internal res

The dead battery of your car provides a potential difference...

The dead battery of your car provides a potential difference of $9.950 \mathrm{~V}$ and has an internal resistance of $1.100 \Omega$. You charge it by connecting it with jumper cables to the live battery of another car. The live battery provides a potential difference of $12.00 \mathrm{~V}$ and has an internal resistance of $0.01000 \Omega$ and the starter resistance is $0.07000 \Omega$. a) Draw the circuit diagram for the connected batteries. b) Determine the current in the live battery, in the dead battery, and in the starter immediately after you closed the circuit

The dead battery of your car provides a potential difference of $9.950 \mathrm{~V}$ and has an internal resistance of $1.100 \Omega$. You charge it by connecting it with jumper cables to the live battery of another car. The live battery provides a potential difference of $12.00 \mathrm{~V}$ and has an internal resistance of $0.01000 \Omega$ and the starter resistance is $0.07000 \Omega$.
a) Draw the circuit diagram for the connected batteries.
b) Determine the current in the live battery, in the dead battery, and in the starter immediately after you closed the circuit

Key Concepts

Electromotive Force (EMF)

EMF is the potential difference generated by a battery or any other power source when no current is drawn. It characterizes the ideal voltage that drives the movement of charges in a circuit and serves as the driving force in electrical systems. This concept is central to understanding how batteries contribute energy to electrical circuits.

Internal Resistance

Internal resistance models the inherent opposition to current flow within a battery or power source. It accounts for the voltage drop that occurs when current flows, making the actual terminal voltage lower than the EMF under load conditions. This concept is crucial for calculating real-world performance of batteries and predicting current distribution in circuits.

Circuit Diagrams

Circuit diagrams offer visual representations of electrical circuits by using standardized symbols to depict components such as batteries, resistors, and connections. They serve as essential tools for understanding, planning, and analyzing the behavior of circuits, enabling one to see how each element is interconnected.

Kirchhoff's Laws

Kirchhoff's Laws include the loop rule, which states that the sum of voltage drops and rises around any closed circuit loop must equal zero, and the junction rule, which states that the total current entering a junction must equal the total current leaving it. These rules provide a foundation for analyzing complex circuits by setting up equations that account for the interactions between multiple components.

Series and Parallel Circuits

Understanding series and parallel circuit configurations is essential for analyzing how current and voltage distribute among components. In a series circuit, components are connected in a single path causing currents to be equal and resistances to add up, whereas in parallel circuits, voltage remains consistent across branches while currents split among different paths. This differentiation is key in circuit design and analysis.

Transcript

00:01 High in the given problem potential difference provided by the dead battery of the car is v1, let it be v1 and this is equal to 9 .950 volt.

00:29 Its internal resistance that is given as r1 is equal to 1 .10 oom.

00:45 On the other hand, potential provided to it by live battery, that is v2, is equal to 12 .00 volt and its internal resistance of the life battery is 0 .01 .0 only.

01:25 Then the resistance of the starter that is given as capital r is equal to 0 .070 0 .0.

01:43 There is one more 0.

01:45 So first of all, in the first part of this problem, we have to draw a circuit diagram of this arrangement of the two car batteries.

01:55 One is dead.

01:56 Another is live and one is starter so the two batteries are in parallel in such a manner that this dead battery should be getting a supply with the help of this live battery that's why their positive terminals are connected together then their internal resistance are shown here r1 r2 this was v2 now the starter should also be in parallel with them so that it may get a total net potential this is the resistance of the starter now suppose current i1 is coming out of this dead battery current i2 is coming out of this live battery here these terminals are a b c d and e and f so at this terminal at this junction e the current will join to give this i and using junction rule at this junction e first of all the circuit diagram which has been asked in first part that is as shown here in this figure.

03:33 Now in the second part of the problem we have to find all the currents coming out of both the batteries and passing through the starter.

03:45 So to do this first of all using junction rule, kirchov's junction rule at the junction e we get this i is equal to i 1 plus i 2 we can make it equation number 1 now this i which will be passing through r means this is i 1 plus i 2 that will come here at junction f and again will be divided into two parts i 2 passing through this v2 and i 1 passing through this v1 now using kirchhoff's loop rule in closed loop a e e fda here this is a e fda fda we can consider it to be loop one also here this now in this loop the krechof's loop rule rule says algebraic sum of all the potential drops.

05:11 Here there are two potential drops, one across r1 and another across r2.

05:15 This algebraic sum of potential drops should be equal to algebraic sum of emfs.

05:20 Here there are two sources of emfs, v1 and v2.

05:23 Now for the sign convention, this i1 is passing through r1 in counterclockwise direction.

05:30 So this potential drop, i1, r1 will be taken as negative.

05:34 Now this i2 is passing through r2 in this closed loop in clockwise direction.

05:40 So here i2 into r2 this potential drop will be taken as positive.

05:44 Similarly, v1 is sending its current in counterclockwise direction...