Consider the circuit below. The battery has an emf of ε=30.00 V and an internal resistance of r=

Consider the circuit below. The battery has an emf of...

Key Concepts

Ohm's Law

Ohm's Law is a foundational principle in electrical circuits that relates voltage (V), current (I), and resistance (R) through the equation V = IR. This law is essential for analyzing circuits as it allows one to compute any one of these quantities if the other two are known. It is used to determine the current flowing through a resistor when the voltage across it is given, and vice versa.

Series and Parallel Circuits

The concept of series and parallel configurations is used to simplify complex resistor networks by reducing them to a single equivalent resistance. In a series circuit, resistances add directly, while in a parallel circuit, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances. This simplification is critical for analyzing how current divides in circuits and determining the overall response of the circuit.

Internal Resistance of a Battery

Internal resistance is the inherent resistance present within a battery that affects its performance by causing a voltage drop when current flows. This concept is important in practical circuit analysis as it causes the terminal voltage of the battery to be lower than its electromotive force (emf) when a load is connected. Accounting for internal resistance allows for a more accurate determination of circuit currents and power dissipation.

Kirchhoff's Laws

Kirchhoff's Circuit Laws, which include Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL), provide methods for analyzing complex circuits. KCL states that the total entering current at a junction equals the total leaving current, while KVL states that the sum of all voltage drops around any closed loop in a circuit must equal zero. These laws are essential for determining current distributions and potential differences in circuits.

Power Dissipation in Resistive Circuits

Power dissipation in resistive elements refers to the conversion of electrical energy into heat energy, which is calculated using formulas such as P = IV, P = I²R, or P = V²/R. Understanding power dissipation is crucial for ensuring that components operate within their safe limits and for analyzing the efficiency of electrical circuits.

Transcript

00:01 For this question, question 69, we want to first find what is the overall equivalent resistance of the circuit and from there find the current from the battery.

00:18 Now to do that, we will need to simplify the resistors that are in parallel.

00:25 What we have to do is to add them up together.

00:27 So for the r1 and r2, r1, r2 portion, we can simplify them by adding them up together in resprocals.

00:39 So 1 over 9 plus 1 over 18, inverse to find the effective resistance across this particular part of the circuit.

00:56 We get 6 oms.

00:58 We do the same for the r3r4 portion.

01:05 So this 1 over 10 plus 1 over 10, we get 5 oms.

01:14 After which we can find all the equivalent resistance by summing them together, since they are all now in series.

01:23 So plus r5.

01:25 So we get 6 oms plus 5 plus 8 oms from the r5 plus 1 ome from the internal resistance of the battery.

01:36 So 6 plus 5 plus 8.

01:38 This one, we get 20 oms.

01:41 This is the equivalent resistance of the entire circuit.

01:47 And from there we can find out what is the current.

01:54 By taking i equals to v over r.

01:59 V, which is the emf of the battery, 30 volts, divided by the total resistance of the circuit, which is 20 oms gets 1 .5 ampers.

02:19 Now the next part we want to do is to find the potential drop across each resistor and to do that we will need to know what is the in fact the across all of these resistors we can use v equals to ir to find the potential drop.

02:55 For the parallel circuits, we can use the effective resistance to find what is the potential drop because they both share the same potential drop, right, since they are connected in parallel.

03:11 So let us start off with the easiest one, which is the potential drop across r5...

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