Base your answers to questions 51 through 54 on the diagram below, which shows three resistors c

step 1 Three resistors are arranged in series. R sub 1 and R sub 3 are given, but R2 is not. The connec

Base your answers to questions 51 through 54 on the diagram...

Key Concepts

Equivalent Resistance

Equivalent resistance is the single resistance that can replace a complex network of resistors without changing the overall current and voltage characteristics of the circuit. It is calculated by combining resistors that are arranged in both series and parallel configurations into one effective value, simplifying circuit analysis.

Series Connection

A series connection occurs when resistors are connected end-to-end such that the same current flows through each resistor consecutively. The overall resistance in a series circuit is the sum of the individual resistances, making it straightforward to calculate.

Parallel Connection

A parallel connection occurs when resistors are connected so that each resistor is connected across the same two points, providing multiple paths for current flow. The calculation for equivalent resistance in a parallel circuit involves taking the reciprocal of the sum of the reciprocals of the individual resistances.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that relates voltage (V), current (I), and resistance (R) through the equation V = IR. This law is crucial for analyzing how changes in resistance affect current and voltage in a circuit.

Transcript

00:01 Three resistors are arranged in series.

00:04 R sub 1 and r sub 3 are given, but r2 is not.

00:08 The connection is connected to a voltage source of 15 volts.

00:14 And as shown in the diagram, there is a current of half an ampere.

00:18 Question 51, what is the equivalent resistance of the circuit? four choices are given to us.

00:25 To help us answer the question, we need to apply the characteristics of the electrical quantities in resistors in series.

00:36 So we have it here in red ink, wherein you have the total resistance or the equivalent resistance is equivalent to the summation of the resistances.

00:47 You also have here the total current, which is equivalent to the individual currents.

00:52 And the total voltage is the sum of the individual voltages.

00:56 So i hope you agree with me that our main working equation, of course, is the first one, this one.

01:03 However, our problem is we do not know resistance to yet.

01:07 So we need to find resistance to first before using this equation for equivalent resistance.

01:16 Okay.

01:17 So since this is series, resistors in series, we know that this 0 .5 ampere is the same current that flows through resistor 2 and the same current that flows through resistor 1.

01:32 Therefore, we can determine the voltage across resistor 1 and determine the voltage across resistor 3 so that you'll be able to determine voltage across 2 and thereby get resistance 2.

01:48 Okay, so let's do that step by step.

01:50 First, let's determine voltage across resistor 1 first, applying oms slope.

01:57 So it's just i1 times r1.

02:00 We have half an ampere times 5 oms.

02:05 So the voltage across resistor 1 is 2 .5 volts.

02:12 In other words, out of the 15 volts, it's only 2 .5 that is across r1.

02:21 So the series circuit here is actually a voltage divider because the 15 volts here gets to be distributed across each resistance.

02:32 Okay.

02:33 Now let's find the voltage across resistor to applying the same logic.

02:40 So this is still the current.

02:42 I'm sorry, this should be voltage 3.

02:45 Okay.