The current in a circuit is tripled by a connecting a 500-ohm resistor in parallel with the resistance of the circuit. Determine the resistance of the circuit in the absence of the 500-ohm resistor.
2007-03-02 08:17:49 · 6 answers · asked by hpage 3 in Science & Mathematics ➔ Physics
Write Ohm's law for both circuits:
V = I * R and V = 3*I*[(500*R)/(500+R)]
V is constant so :
I * R = 3 * I * [(500 * R)/(500 + R)]
Divide both sides by I
R = 3 * [(500 * R)/(500 + R)]
Solving for R
500R + R^2 = 1500R
500 + R = 1500
R = 1000
2007-03-02 08:35:23 · answer #1 · answered by tipp10 4 · 0⤊ 1⤋
While 1000 ohms is correct, let me offer a much more simple way of doing the parallel resistance thing. Multiply the 1000 ohms times the 500 ohms, then divide the result of that by 1500, or the added combination of the 2 resistor values. That would be R1xR2/R1+R2. It works out just as well, and is a lot less confusing. You'll find that formula in the ARRL Handbook for Radio Amateurs. If you have a dozen resistors in parallel, it still works. Just take the first 2 resistors as R1 and R2, solve for that combination, and then use the result as R1, and continue to solve for the complete combination of the 12, or however many resistors there are. Keep it simple, and uncluttered, things get easier that way.
2007-03-02 23:23:00 · answer #2 · answered by Anonymous · 0⤊ 1⤋
If the total current is three times the initial current then for a given voltage (V) the current in the 500 ohm resistor is twice that of the original circuit.
Therefore the resistance of the circuit is twice that of the 500 or 1000 ohm.
1/R (total) = 1 / R (1) +1 R (2)
1/R (total) = 1/500 + 1/ 1000 = 3/1000
R (total)= 1000/3 =333.3..ohm or one third of R (circuit).
2007-03-02 08:29:29 · answer #3 · answered by a simple man 6 · 1⤊ 1⤋
let's use admittance instead of resistance.
in this case Yo is the original admittance.
when you added the 500 ohm resistance the admittance tripled.
therefore:
Yo + Y500 = 3Yo where Y500 is the admittance of a 500 ohm resistor.
we therefore get 2Yo = Y500
or
Yo = 0.5Y500
flipping over to get R:
Ro = 2*R500
Ro = 1000 ohms.
2007-03-02 10:07:28 · answer #4 · answered by Anonymous · 0⤊ 1⤋
1000 ohms
V=IR, V is constant, I increases by factor of 3 when additional resistance added in parallel. R in parallel is equal to 1/R1 + 1/R2.
Solve for R1 when R2 = 500 ohms...
2007-03-02 08:23:01 · answer #5 · answered by Anonymous · 1⤊ 1⤋
i think it would just be 1000 ohm's because 500 * 3 = 1500 ohm's but its Say's there is an absence of 500 ohm's so there for it would just be the 1000 ohms
2007-03-02 08:22:39 · answer #6 · answered by tommy two tone 2 · 1⤊ 2⤋