Consider the circuit shown in Figure P 18.10. (a) Calculate...

Consider the circuit shown in Figure P 18.10. (a) Calculate the equivalent resistance of the $10.0-\Omega$ and $5.00-\Omega$ resistors connected in parallel. (b) Using the result of part (a), calculate the combined resistance of the $10.0-\Omega, 5.00-\Omega,$ and $4.00-\Omega$ resistors. (c) Calculate the equivalent resistance of the combined resistance found in part (b) and the parallel $3.00-\Omega$ resistor. (d) Combine the equivalent resistance found in part (c) with the $2.00-\Omega$ resistor. (e) Calculate the total current in the circuit. (f) What is the voltage drop across the $2.00-\Omega$ resistor? (g) Subtracting the result of part (f) from the battery voltage, find the voltage across the $3.00-\Omega$ resistor. (h) Calculate the current in the $3.00-\Omega$ resistor.

Key Concepts

Voltage Drop

Voltage drop refers to the reduction in voltage as electric current flows through the resistance in a circuit. It is a direct application of Ohm's law and is essential for determining how the total supplied voltage divides among different components in a circuit.

Equivalent Resistance Calculation

This concept involves combining resistors arranged in series or parallel to replace them with a single resistor that has the same effect on the circuit. Calculating the equivalent resistance helps in simplifying the circuit, making it easier to apply other analysis techniques such as Ohm's law.

Ohm's Law

Ohm's law is a fundamental principle in circuit theory that relates voltage, current, and resistance through the equation V = IR. It is used to calculate any one of these quantities when the other two are known, providing a powerful tool for analyzing and predicting circuit behavior.

Resistors in Series

In a series configuration, resistors are connected one after the other so that the same current flows through each resistor. The overall or equivalent resistance is simply the sum of the individual resistances. This concept is essential in circuit analysis because it simplifies the network into a single resistance that experiences the entire current.

Resistors in Parallel

When resistors are connected in parallel, they share two common nodes which means that the voltage across each resistor is the same. The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances. This method of grouping resistors is crucial for analyzing complex circuits as it reduces multiple pathways into one effective resistance.

Transcript

00:01 In this particular circuit, we need to find the effective resistance of ten om and phi -oam.

00:08 So when we start with step a here, since ten oom and phi -oam are in parallel because the current is getting splited between them, so what we can say, let r1 is a combination of ten -oam parallel to phi -oom.

00:32 Therefore, we can get the value of r1 by using formula 10 multiplied by 5 and this combination is divided with 10 plus 5.

00:46 Since we use the formula r1 into r2 upon r1 plus r2 to find the effective resistance of parallel combination.

00:57 Therefore, we get the value of this combination as 3 .33 ooms.

01:03 So in this case the value of r1 which is a parallel combination of 10 -hom and 5 -oam is 3 .33 home.

01:13 And this is our first answer.

01:18 Now let's move towards step b in which we need to find the combined resistance of 10 -hom, 5 -oom and 4 -oom.

01:29 So we'll assume that let combined resistance of 10 -oom, phi -oom, and 4 om b r2 therefore we'll just draw the diagram first to understand the concept behind it this is 2 oom which is given now value of r1 is 3 .33 oms which is in series with 4 oms and this combination is in parallel with 3 oms and the battery of 8 volt is attached to it with current is considered as i.

02:36 Now this 3 .33 and 4 om both are in series.

02:42 Therefore the value of r2 will be value of r1 plus 4 oms.

02:49 And value of r1 we have already got it as 3 .33 oms plus 4 oms.

02:57 So the answer is 7 .33 oms.

03:01 Therefore the value of r2 is 7 .33 oms.

03:09 This is the combined resistance of 10 -on, 5 -oom and 4 -oom.

03:18 Now step c, let's draw the circuit first, which is 2 oms.

03:26 Now we got the combined resistance, r2 as 7 .33 oms, which is in parallel with 3 oms and the 8 volt battery attached to it.

03:43 Now in this step, they have asked the combined resistance of r2 and 3 -oom.

03:53 So let the combined resistance of r2 and 3 -o be r3.

04:12 Therefore, to find the value of r3, we make use of formula which is used to find parallel combination.

04:26 So it is 7 .33 multiplied by 3 divided by 7 .33 plus 3.

04:34 So here we get the value as 2 .13 oom.

04:41 Therefore the value of r3 is equal to 2 .13 oom.

04:48 This is answer for step 3 and this value is the combined resistance value of r2 and 3 oom.

05:00 Now, moving towards step d.

05:07 We need to find the combined register of r3 and 2 -oom now.

05:13 So, we'll just draw the circuit first.

05:17 So this is 2 oms.

05:19 Now we have already got the combination, which is 2 .13 -oom, which is the value of r3...

Please give Ace some feedback