Calculating total current

Question

I've got this circuit and I'm wondering if my logic is messed up when calculating current.

I calculate total current in the circuit by finding resistances of the resistors in parallel and then adding those in series with the 800 Ω resistor.

So:

$$ R_{top} = \left( \frac{1}{4k} + \frac{1}{2k} \right)^{-1} \Omega = 1333.333 \; \Omega $$

Then the bottom parallel:

$$R_{bottom} = \left( \frac{1}{400} + \frac{1}{1.6k} \right)^{-1} \Omega = 320 \; \Omega $$

Then I add those 2 resistors in series with the \$800 \Omega\$ resistor to get a total circuit resistance of \$2453.33 \Omega\$

Then I say

$$ I=\frac{V}{R} = \frac{8}{2453.333} A = 3.26 \; {mA} $$

Does this work out? Or is my logic incorrect?

Answer 1

^{simulate this circuit – Schematic created using CircuitLab}

No, your reasoning is perfect. BTW, you should use a simulator to check your results if you are not sure. If you will dedicate your entire life to electronics, you better start using LTSpice or some simulator that be more sophisticated than the one is offered on this site.