Consider the circuit shown in figure. Assume I = 0.82 A. What is the value of resistor R?
My Analysis: Since resistors are in parallel, the voltage should be the same throughout the circuit.
Total current known = I1 + I2 = 0.82A + 2A
But the voltage is not known.
Total Resistance = (1/10 + 1/15 + 1/R )^-1
V = 6R/(6+R) * (2.82A)
I need help to solve this. Thank you.
- billrussell42Lv 72 months agoFavorite Answer
I'm assuming the drawing is actually as shown below. As originally shown, the connections are ambiguous. The dots are needed to indicate a connection, not a crossover.
Question: Assume I = 0.82 A. What is the value of resistor R
Best way to do these problems is to solve what you can, using ohms law and kirchoff's laws.
for 10 Ω resistor,
E = IR = 0.82 x 10 = 8.2 volts
this same voltage is across each resistor.
current thru 15 Ω is 8.2/15 = 0.547 amp
sum of the currents thru the 3 resistors has to add up to 2 amps.
current thru R is 2 – 0.82 – 0.547 = 0.633 amps
R = E/I = 8.2/0.633 = 12.9 Ω
- oubaasLv 72 months ago
I(10) = 0.82
I(15) = 0.82*2/3 = 1.64/3 A
I(r) = 2.00-(2.46/3+1.64/3) = 2-4.10/3 = 1.9/3 A ( ≅ 0.6(3) )
r = 0.82*10/(1.9/3) = 8.2*3/1.9 = 24.6/1.9 ohm ( ≅ 12.95 )
- oldschoolLv 72 months ago
You know the voltage across the left 10Ω = 10Ω*0.82A = 8.2V
Thus that is also the voltage across the 15Ω. Therefore the current in the 15Ω =
8.2V/15Ω = 41/75 = 0.5467
Thus 2A - 0.82A - 0.5467A = 19/30 = 0.63333A is the current in R
But we know the voltage across R = 8.2V since it's in parallel with the 10 and 15Ω
R = 8.2/(0.63333) = 8.2/(19/30) = 3*82/19 = 246/19 = 12.95Ω or about 13Ω <<<<