Well, $\text{R}_3$, $\text{R}_4$, $\text{R}_5$ and $\text{R}_6$ are in parallel and they are in series with $\text{R}_1$ and $\text{R}_2$. simulate this circuit – Schematic created ...

Well, let's make a mathematical closed solution. I know that this is maybe above the OP's knowledge, but I think it is important to show it in combination with the other answers given. We know that ...

Well, the definition of susceptance is the following: $$\text{susceptance}=\Im\left(\text{admittance}\right)=\Im\left(\frac{1}{\text{impedance}}\right)\tag1$$ In formula form: $$\text{B}=\Im\left(\... View answer Accepted answer 7 votes Well, generally we have two things that we look at: dB/decade:$$\lim_{\omega\to\infty}\left(20\log_{10}\left|\underline{\mathscr{H}}\left(10\omega\text{j}\right)\right|-20\log_{10}\left|\underline{\...

Well, mathematically speaking we can write: $$\mathcal{H}\left(\text{s}\right)=\frac{\text{sL}}{\text{sL}+\text{R}}\tag1$$ Using $\text{s}=\text{j}\omega$, we get: $$\left|\underline{\mathcal{H}}\... View answer Accepted answer 5 votes First of all, you wrote: "defined by the current across" but the current is trough a component, voltage is across. Well, we are trying to analyze the following circuit: simulate this circuit – ... View answer Accepted answer 4 votes Well, using the voltage divider formula we can see that:$$\text{v}_+\left(\text{s}\right)=\frac{\text{R}}{\text{R}+\frac{1}{\text{sC}}}\cdot\text{v}_\text{in}\left(\text{s}\right)\tag1\text{v}_-...

Notice, that $\forall x\in\mathbb{R}$: $$\left|\exp\left(xi\right)\right|=1\tag1$$ Because: $$\left|\exp\left(xi\right)\right|=\left|\cos\left(x\right)+\sin\left(x\right)i\right|=\sqrt{\underbrace{\... View answer 4 votes Well, we are trying to analyze the following circuit: simulate this circuit – Schematic created using CircuitLab When we use and apply KCL, we can write the following set of equations:$$\text{...

Well, we know that: $$\mathcal{H}\left(\text{s}\right):=\frac{\text{V}_\text{out}\left(\text{s}\right)}{\text{V}_\text{in}\left(\text{s}\right)}=\frac{\frac{1}{\text{sC}}}{\frac{1}{\text{sC}}+\text{R}... View answer Accepted answer 3 votes Well, we are trying to analyze the following circuit: simulate this circuit – Schematic created using CircuitLab When we use and apply KCL, we can write the following set of equations:$$\text{...

The voltage-current relation in a capacitor in the time domain is given by the following formula: $$\text{I}\left(t\right)=\text{C}\cdot\frac{\partial\text{V}\left(t\right)}{\partial t}\tag1$$ So, ...

Well, we are trying to analyze the following circuit (assuming an ideal opamp): simulate this circuit – Schematic created using CircuitLab When we use and apply KCL, we can write the following ...

Well, according to Ohm's law we know that: $$\text{V}_\text{R}\left(t\right)=\text{I}_\text{R}\left(t\right)\cdot\text{R}\tag1$$ And the power in a resistor is given by: $$\text{P}_\text{R}\left(t\... View answer 3 votes Well, let's make a mathematical closed solution. I know that this is maybe above the OP's knowledge, but I think it is important to show it in combination with the other answers given. The Shockley ... View answer Accepted answer 3 votes Well, the impedance of your circuit is given by:$$\underline{\text{Z}}_{\space\text{in}}=\frac{\text{R}\cdot\text{j}\omega\text{L}}{\text{R}+\text{j}\omega\text{L}}=\frac{\text{R}\cdot\text{j}\omega\...

Well, using Laplace transform we can see that: $$\text{I}_\text{in}\left(t\right)=\mathscr{L}_\text{s}^{-1}\left[\frac{\hat{\text{u}}\omega}{\text{s}^2+\omega^2}\cdot\frac{1}{\text{R}+\text{sL}}\right]... View answer 3 votes First, I will present a method that uses Mathematica to solve this problem. When I was studying this stuff I used the method all the time (without using Mathematica of course). Besides that the answer ... View answer 3 votes Well, we have the following circuit: simulate this circuit – Schematic created using CircuitLab When analyzing a transistor we need to use the following relations:$$\text{I}_\text{E}=\text{I}...

Well, let's solve and show this mathematically. We are trying to analyze the following circuit (assuming an ideal opamp): simulate this circuit – Schematic created using CircuitLab When we use ...

Well, we have the following circuit: simulate this circuit – Schematic created using CircuitLab When analyzing a transistor we need to use the following relations: $$\text{I}_\text{E}=\text{I}... View answer 3 votes Well, we have the following circuit: simulate this circuit – Schematic created using CircuitLab When analyzing a transistor we need to use the following relations:$$\text{I}_\text{E}=\text{I}...

Well, if we are not looking for the transient behavior of the circuit we can use the complex method to find the answer. First, we can find the current trough $\text{R}_2$ using the current divider ...

Your third equation is only correct, if and only if $\sigma=0$. Well, when we state Euler's formula $\forall\space x\in\mathbb{R}$: $$\exp\left(x\text{j}\right)=\cos\left(x\right)+\text{j}\sin\... View answer 2 votes Well, the transfer function of the circuit is given by:$$\mathscr{H}\left(\text{s}\right):=\frac{\text{V}_\text{o}\left(\text{s}\right)}{\text{V}_\text{i}\left(\text{s}\right)}=\frac{\frac{1}{\text{...

Well, the current supplied by the source is given by: $$\text{i}_\text{i}\left(t\right)=\mathscr{L}_\text{s}^{-1}\left[\frac{\hat{\text{u}}}{\text{s}}\cdot\frac{1}{\text{R}+\left(\text{sL}\space\text{|... View answer 2 votes Well, when we have the following circuit: simulate this circuit – Schematic created using CircuitLab It is not hard to see that:$$\underline{\text{V}}_{\space\text{out}}=\frac{\text{R}\text{||}...

First, I will present a method that uses Mathematica to solve this problem. When I was studying this stuff I used the method all the time (without using Mathematica of course). Well, we are trying to ...

Well, the angle of the output voltage can be found using the voltage divider formula: \varphi=\arg\left(\frac{4\text{||}\left(-2\text{j}\right)}{2+12\text{j}+\left(4\text{||}\left(-2\text{j}\right)\...