Solving Resistor Circuits - Online Tutor, Practice Problems & Exam Prep

To solve complex circuit problems, understand that resistors can be in series or parallel. In series, current remains constant across resistors, while in parallel, voltage is constant. Use Ohm's law, V = I⁢R, to find unknown values. Start by simplifying the circuit to one equivalent resistor, then calculate voltage and current for each resistor, ensuring to apply Kirchhoff's laws for current conservation. This systematic approach helps in accurately determining circuit parameters.

Solving Resistor Circuits

Hey, guys. So in this video, we're going to talk about how to solve more complicated circuit problems. Let's check it out. Alright. So in some circuit problems, you'll be asked to find not just the equivalent resistance but also the current I and the voltage V of different resistors. Alright, so let's see how we do that. But first, let me remind you that resistors can be connected in series or in parallel. And if they're in series, this is the equation you use to find the equivalent resistance. This is the equation for equivalent resistance in parallel. Remember that in parallel there are also 2 shortcut equations you can use, 2 shortcuts. So this is old news. What's new here is this stuff here. Right? And when you have resistors in series, they will share current with each other. They will share current with each other. So for example, if I have a 1 ohm resistor, 2 ohms, and 3 ohms, and if I know that this current here is 2 amps, then I know if I'm given the current here is 2 amps, then I know that this here has to be 2 amps. And then I know that this here also has to be 2 amps because they're in a series. The current's flowing this way. It has nowhere to go, so it has to just flow with a constant 2 amps. So they share currents with each other. Cool. Now you need to remember that but you also have to remember that they share current with the equivalent resistor as well. So they share current with the equivalent resistor. What does that mean? Well, if I combine these, I just add them. So I have 1, 2, and 3. This is a 6 ohm resistor. But this 2 here is not only the same for these guys, but it's also the same here. So I'm going to know that this has to be a 2-amp current going through this resistor. So not only is the current the same with each other when you're combining in series but also with the combined merged resistor. K? Very important. One way to think about this is that these guys combine to form the equivalent resistor, and the equivalent resistor will inherit the current because it's coming from a series combination. In parallel, it's not current, it's the voltage that will be the same. K? So the voltage will be the same with each other and also with the equivalent resistor. So let's say this is a 9 ohm resistor, 9 ohm resistor, 9 ohm resistor. You may remember from the shortcut that if I have 3, 9 ohms, the equivalent resistance would just be 9 ohms divided by 3 because there are 3 of them. So the equivalent resistance is 3. That's old news. But let's say I know that this is let's say I know that this is 5 volts. Well, if this guy is 5 volts, it must follow that this guy right here is also 5 volts and this guy here is also 5 volts. Because if they are in parallel, which they are, they have to share the same voltage with each other. And not only with each other but also with the merged equivalent resistor. So the voltage here would also be 5 volts. You can think that when you combine them in parallel, the equivalent resistor will inherit the voltage. K? These points are super important for you to remember. Please do not forget. Now that's important for you to solve the problems. Now here are the 3 steps that you're going to use in solving all of these problems. We're going to be very systematic about this, very systematic. Cool? The first one is you're going to get, you're going to get some sort of weird resistor network here like this and you're going to collapse, 1 equivalent resistor. And we're going to do this using the techniques we already talked about.

So this is old news. Okay? This is old, you know how to do this. Then you're going to find voltage and currents on the equivalent resistor. Once you get down to 1 resistor, you're going to be able to find the voltage and the current on it. And by the way, you're going to do this using Ohm's law, \( v = IR \), which combines currents and voltage with resistance. K? This is old because we've seen \( v = IR \) and it's also really easy. It's a very quick step. Now the hard part is step 3 where we are going to work backwards noting voltage and current on each resistor. Now don't worry about what that means yet. I'm going to show you and the best way to show you is just by doing an example. K? So let's walk through this simple example here and we're going to use these steps to find the current and voltage across each one of these resistors. K? So let's draw small here because we're going to need a lot of space. So the first thing we're going to do, remember from the rules up there, is that we're going to get everything down to 1 resistor. And you know how to do this. The first place I'm going to start is by combining these 2 in parallel. K? I'm going to combine these 2 in parallel. So I'm going to draw the circuit here in black and then circuit here in black. I'm going to leave some space there. This is the 6 ohm resistor and this is the 10 volt battery right here. And this is the combination of the combination of the 2 with the 1. I'm going to do one of these and I'm going to write here that this is a parallel merge. K?

What is current and voltage across each resistor below?

• A. V_2Ω=5.0 V, i_2Ω=4.44 A;
  V_1Ω=5.0 V, i_1Ω=2.22 A;
  V_3Ω=5.0 V, i_3Ω=6.67 A
• B. V_2Ω=6.67 V, i_2Ω=0.500 A;
  V_1Ω=3.33 V, i_1Ω=0.500 A;
  V_3Ω=10.0 V, i_3Ω=2.23 A
• C. V_2Ω= 1.82V, i_2Ω=0.908 A;
  V_1Ω=1.82 V, i_1Ω=0.908 A;
  V_3Ω=8.18 V, i_3Ω=1.36 A
• D. V_2Ω=6.67 V, i_2Ω=3.33 A;
  V_1Ω=3.33 V, i_1Ω=3.33 A;
  V_3Ω=10.0 V, i_3Ω=3.33 A

Find Current of One Resistor

Hey, guys. So in this example, I want to show you how some of these problems are actually deceivingly simple. They look complicated, but they're very straightforward. This is an example of them. So in this question, instead of asking for everything, we're being asked for just one thing, which is what is the current through the 3 ohm resistor, which is this guy here. So that's all we need to know. Let's call this the current through the 3 ohm. What is it? K? Well, remember, the equation that connects all these variables is Ohm's law, V=IR. So you can find I as long as you have V and R. If you solve for I, you get VR. I know the resistance is 3 ohms. So really all I need is the voltage. Now you may also remember that the voltage is the same in parallel. And it's not just the same between resistors; it's the same for any circuit elements. So the voltage across these two points is the same through that branch. It's the same as the voltage across these points is the same through that branch is the same as the voltage across these two points. And it's the same for this voltage, and it's the same for the voltage between these two resistors. So because the voltage through this battery is 5, I can say that the voltage on the 3 ohms has to be 5 as well because they're parallel. So that's it. This voltage is 5 volts. I can divide the 2, and the answer is gonna be 1.67 amps, and we're done. Super straightforward, but you have to be able to recognize certain properties. Okay? So some of these questions are gonna be very long, and some of them are gonna be tricky and simple. So you gotta be ready for both. Let's keep going.

What is the voltage of the battery below?

• A. 1.71 V
• B. 5.25 V
• C. 11.3 V
• D. 13.0 V

Here’s what students ask on this topic:

How do you find the equivalent resistance in a series circuit?

To find the equivalent resistance in a series circuit, simply add the resistances of all the resistors together. The formula is:

$R_{\mathrm{eq}}=R_1+R_2+R_3+...+R_n$

where $R_{\mathrm{eq}}$ is the equivalent resistance, and $R_1$, $R_2$, $R_3$, ..., $R_n$ are the resistances of the individual resistors.

How do you calculate the equivalent resistance in a parallel circuit?

To calculate the equivalent resistance in a parallel circuit, use the reciprocal formula:

$R_{\mathrm{eq}}=\frac{1}{\frac{1}{R_1}}$

where $R_{\mathrm{eq}}$ is the equivalent resistance, and $R_1$, $R_2$, $R_3$, ..., $R_n$ are the resistances of the individual resistors.

What is Ohm's Law and how is it used in solving resistor circuits?

Ohm's Law states that the voltage (V) across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R). The formula is:

$V=IR$

In solving resistor circuits, Ohm's Law is used to find unknown values of voltage, current, or resistance. For example, if you know the current and resistance, you can find the voltage. Similarly, if you know the voltage and resistance, you can find the current.

How do you apply Kirchhoff's laws to solve complex resistor circuits?

Kirchhoff's laws include the Junction Rule and the Loop Rule. The Junction Rule states that the total current entering a junction equals the total current leaving the junction. The Loop Rule states that the sum of the voltage gains and drops around any closed loop in a circuit must be zero. To solve complex resistor circuits, use these laws to set up equations based on the currents and voltages in the circuit. Solve these equations simultaneously to find the unknown values.

What are the steps to solve a complex resistor network?

To solve a complex resistor network, follow these steps:

1. Simplify the circuit to one equivalent resistor by combining resistors in series and parallel.
2. Calculate the voltage and current for the equivalent resistor using Ohm's Law.
3. Work backwards to find the voltage and current for each individual resistor, applying Kirchhoff's laws as needed.

This systematic approach ensures accurate determination of circuit parameters.