Consider the circuit shown in (Figure 1). Assume I = 0.94 A. What is the value of resistor R?

oldschool

You know the voltage across the left 10Ω = 10Ω*0.94A = 9.4V Thus that is the voltage across the 15Ω and R. Therefore the current in the 15Ω = 9.4/15 = 94/150 = 47/75 A Kirchoffs current law says current in = current out and there 2A entering and 0.94+47/75 = 141/150+94/150 = 235/150 = 47/30 leaving. Thus 2A = 60/30 and (60-47)/30=13/30 A must go right and down into R. We know the voltage across R = 9.4V = the voltage across the 15Ω and = that across the 10Ω. Now we can write: 9.4V = 13/30 A *R. Therefore R = 9.4/(13/30) = 282/13 282/13 Ω = 21.7Ω = R or 22Ω with 2 significant digits.

qrk

Since you know the current flowing through the 10 ohm resistor, you can calculate the voltage across the resistor (E = I * R). Now that you know the voltage across all three resistors, you can calculate the combined resistance off all three resistors in parallel and solve for R. (hint: R = E / I) -- or an easier way -- Since you know the current through the 10 and 15 ohm resistors, you can calculate the current through R and figure out its value.

Philomel

E=I*R = .94*10=9.4v. I=E/R = 9.4/15 = .627A R= E/I = 9.4/(2-(.627+.94) = 9.4/.433 = 21.7Ω. R=21.7Ω Very good problem.