What is the current through this resistor (2R)?

Question

Given that V = 10.00 V and R = 5.000 ohms, can you determine the size of current through the resistor 2R. You may use whichever method you like but I want to see how many people can do it with kircchoff's rules.

http://www.geocities.com/trunks11111/resistors.jpg

Answer 1

Draw the diagram. In each of the four little loops, draw a current loop. So you have I1, I2, I3, and I4.

Over each resistor, the voltage drop is the resistance times the net current. So if two loops go through that resistor in opposite directions, the voltage drop is the difference.

Now you know that the sum of the voltage changes around a loop is zero. The voltage lift/drop across a battery is given. Use what I told you above to get the voltage drop across a resistor. Now you have four equations and four unknowns (I1,2,3,4). Once you have the currents, you can find the net current across the resistor in question and find the voltage drop across it.

These problems are tedious, but if you practice a bunch, you can get the hang of them.

Answer 2

1st set V3 and V10 to dead-short, and solve for current through V2. Iv2 = 6/(5R)

Then do likewise for the other 2 voltage sources.
Iv3 = 7/(2R)
Iv10 = 4/R (that component which only affects 2R)

Then by superposition, the total current flowing through 2R is 4/R-7/(2R), which is 1/(2R)
.

Answer 3

V = I*R or in this case, I = V/R.

The current (in Amps) is equal to the Voltage divided by the resistance.

10 Volts divided by 2*R or 2*5 or 10 is 10/10 or 1 Amp.