1. For the RL circuit find the current I after t seconds if I(0) = 2 E= 6V R= 3
ID: 2966559 • Letter: 1
Question
1. For the RL circuit find the current I after t seconds if I(0) = 2
E= 6V R= 3 ohms L= 3H
2. For the RC circuit with sinusoidal power source find the charge Q on the
capacitor after t seconds if Q(0) = 0.
V= 10Sin(t) R= 5 ohms C= 0.2 F
3. When a hot object is placed in a water bath whose temperature is 25 degrees C,
it cools from 100 degrees C to 50 degrees C in 160s. In another bath, the same cooling occurs in
140s. Find the temperature T2 of the second bath.
4. A cup of coffee at 181 degrees is poured into a mug and left in a room at
80 degrees. After 3 minutes, the coffee is 142 degrees. What is the temperature
T of the coffee after 13 minutes?
Explanation / Answer
for 1,2 diagram is required as rl,rc circuits can be series or parallel.
3. dT/dt = k(T-T0)
where T0 is the ambient temerature.
=> On solving, we get T = T0 + (T1-T0)e^-kt where T1 is heat of object at time 0
=>50 = 25 + 75e^-160k => e^-160k = 1/3 => k = 6.8 * 10^-3
T2 = 25 + 75*e^-140k = 25 + 75 * 0.38 = 53.68 C
4. 142 = 80 + 101*e^-180k => e^-180k = 0.613 => k = 2.7*10^-3
T = 80 + 101*e^-780k => T = 936.9 degrees
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