if two resistors of r1 and r2 ohms are connected in parallel in an electriccircuit to make a R ohm resistor, the value of R can be found from the equation 1/R= 1/r1+ 1/r2. if r1 is decreasing at the rate of 1 ohm/s and r2 is increasing at the rate of 0.5 ohm/s.at what rate is R changing when r1=75 phm and r2= 50 ohm.
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To find the rate at which R is changing, we can differentiate the equation 1/R = 1/r1 + 1/r2 with respect to time. This will give us the rate of change of R in terms of the rates of change of r1 and r2.
Differentiating 1/R = 1/r1 + 1/r2 with respect to time (let's call it t), we have:
d(1/R)/dt = d(1/r1)/dt + d(1/r2)/dt
To find d(1/r1)/dt and d(1/r2)/dt, we substitute the given rates of change:
d(1/r1)/dt = -1 (since r1 is decreasing at a rate of 1 ohm/s)
d(1/r2)/dt = 0.5 (since r2 is increasing at a rate of 0.5 ohm/s)
So the equation becomes:
d(1/R)/dt = -1 + 0.5
Simplifying further:
d(1/R)/dt = -0.5
Now, we need to find dR/dt, the rate at which R is changing. We can do this by taking the reciprocal of both sides:
dR/dt = -1/(0.5)
dR/dt = -2
Therefore, the rate at which R is changing when r1 = 75 ohm and r2 = 50 ohm is -2 ohm/s.