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I am trying to find \$v_0\$ in this circuit (voltage across \$R4\$):

schematic

simulate this circuit – Schematic created using CircuitLab

Schematic

The issue I am having is that I would have known that the current going into the 16 ohm resistor would have been the same as the one going in the negative terminal, but that's only if they are both going into the negative terminal. I know that its 0 volts to ground on the right side. And 0 volts in between the + and -.

Can someone help me find \$v_0\$?

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    \$\begingroup\$ electronics.stackexchange.com/questions/127423/… \$\endgroup\$ – jippie Sep 1 '14 at 19:22
  • \$\begingroup\$ Are you familiar with voltage dividers? \$\endgroup\$ – Armandas Sep 1 '14 at 19:29
  • \$\begingroup\$ Not in particular, we have went over them a little bit in Linear Circuit Analysis I, but thats my issue. \$\endgroup\$ – JT Hiquet Sep 1 '14 at 19:29
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    \$\begingroup\$ This is a stupid textbook circuit since a typical op-amp won't be able to supply that kind of current. They should have made them all K ohms. \$\endgroup\$ – Spehro Pefhany Sep 1 '14 at 20:03
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Golden Rules. With negative feedback in place...

  1. No current flows into the input terminals of the opamp
  2. The voltage at the plus terminal equals the voltage at the minus terminal.

Because no current flows into the positive terminal, current must flow from the voltage source, through the series resistors 16 ohm and 24 ohm. So you should be able to figure out that the voltage at the input terminal is 7.5 * 24 / 40 = 4.5V. It follows that the voltage at the negative terminal = 4.5V. Now you've got another voltage divider from the negative terminal through 8 ohms in series with 12 ohms. The voltage across the 12 ohm resistor is therefore 4.5 * 12 / 20 = 2.7V.

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  • \$\begingroup\$ So the node before the 8 ohm resistor has the same voltage as the + side terminal voltage? \$\endgroup\$ – JT Hiquet Sep 1 '14 at 19:34
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From a more practical point of view, this is what you have:

schematic

simulate this circuit – Schematic created using CircuitLab

A voltage divider on the input, a unity gain buffer and a voltage divider at the output.

Voltage divider output is calculated as follows:

$$ Vo = \frac{Vi \times R2}{R1 + R2} $$

Where Vi is 7.5V for the first divider.

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  • \$\begingroup\$ What about the R3 and R4? Do you not worry about those? \$\endgroup\$ – JT Hiquet Sep 1 '14 at 19:35
  • \$\begingroup\$ It's a divider too, so the same formula applies. Just replace R1/R2 with R3/R4. \$\endgroup\$ – Armandas Sep 1 '14 at 19:37

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