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Tom Moynihab
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【Mod Note: moved from technical forum, so homework template is missing】
In a parallel circuit, one branch contains two equal resistors of resistance ##R_1## connected in series. The other branch contains a resistor of resistance ##R_1## in series with an inductor of variable inductance ##L##.
Show that the magnitude ##|V_{AB}|=\frac{V}{2}## and ##\phi=\tan^{-1}\big(-\frac{2\omega LR_1}{R_1^2-\omega^2L^2}\big)##https://gyazo.com/50cbf5ef913b0fc533ebcb0074b3b5a3 (Very sorry for the link, but the image uploader wasn't working for me)
{image inserted by moderator}I have worked out that total impedance =##|Z|=\frac{2R_1(R_1+\omega L)}{3R_1+\omega L}## Which I'm not sure is correct.
I'm thinking that I have to work out what fraction of voltage ##R_1## gets in the ##B## branch, but I'm pretty confused.
Edit: I have managed to prove ##|V_{AB}|=\frac{V}{2}## and am now stuck on the second part, it's only two marks so it shouldn't be difficult, I just don't know what impedance I'm meant to be taking
Any help on this would be really appreciated :)
In a parallel circuit, one branch contains two equal resistors of resistance ##R_1## connected in series. The other branch contains a resistor of resistance ##R_1## in series with an inductor of variable inductance ##L##.
Show that the magnitude ##|V_{AB}|=\frac{V}{2}## and ##\phi=\tan^{-1}\big(-\frac{2\omega LR_1}{R_1^2-\omega^2L^2}\big)##https://gyazo.com/50cbf5ef913b0fc533ebcb0074b3b5a3 (Very sorry for the link, but the image uploader wasn't working for me)
I'm thinking that I have to work out what fraction of voltage ##R_1## gets in the ##B## branch, but I'm pretty confused.
Edit: I have managed to prove ##|V_{AB}|=\frac{V}{2}## and am now stuck on the second part, it's only two marks so it shouldn't be difficult, I just don't know what impedance I'm meant to be taking
Any help on this would be really appreciated :)
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