Question

Consider the circuit shown in the figure below. (Let R1 = 3.00 Ω, R2 = 8.00 Ω, and = 10.0 V.)

(a) Find the voltage across R1.




(b) Find the current in R1.

Answer 1

There are several ways to solve this problem, but I'm assuming you're doing it without using mesh current or node voltage. You can calculate the voltage between R1 and the 2Ω resistor by simplifying those 4 resistors. The 10Ω || 5Ω = 3.33Ω. 11.33Ω || 3Ω = 2.373Ω. Then calculate the V across R1 with \[ Input V\times \left(Parallel R \div Total R \right)\]\[10V\times\left(2.373\div4.373\right)\]
From there it is easy to calculate the current through R1 by ohms law.

Answer 2

i think you could first calculate the total resistance:
Req = 2+ ((10||5)+R2)||R1)
then calculate Iin
I = V/Req
then calculate the voltage drop on the 2ohm resistance, so the voltage across R1 is
V - Iin * 2 = Vr1
and finally by ohm's law:
Ir1 = Vr1 / R1

Answer 3

see thus image

Answer 4

I like using a spreadsheet. It helps with error checking also. To stimulate some peoples greater interest: When analyzing
AC cirduits it generated results that I thought helped me to better tune an equalizer to generate a flatter curve response
by assuming that it was a set of parallel filters. The graphing of results of the frequecy amplitudes was of the greatest
interest.

Answer 5

The 5 ohm and 10 ohm resistors are in parallel and can thus be replaced by a single resistor Ra= (1/10 + 1/5 )-1 = 3,33 ohm

Ra and R2 (in series) can be replaced by a single resistor Rb=(3,33+R2)

Then Rb and R1 in parallel is equivalent to a single resistor Rc=(1/Rb + 1/R1)-1 = \[R1(10 +3R2) / (3(R1+R2) +10)\]
Now that things have been simplified; the voltage across Rc is the same as that of our combined resistors into Rc (a) V(R1)= Rc*E/(Rc + 2)= \[(R1E(10+3R2))/(16R1+6R2+3R1R2+20)\]
Coming back to our initial circuit: The volatge V across R1= R1*I
(b) I= V/R1 = [(R1E(10+3R2))/(R1*(16R1+6R2+3R1R2+20))\]
Numerical Answer:
(a) V= (3*10*(10+3(8))/(16(3)+6(8)+3(3*8)+20) = 5,43 V
(b) I= (3*10*(10+3(8))/3((16(3)+6(8)+3(3*8)+20))=1,81 A