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Electric Circuits questions please!?
1. a)The potentiometer extends between positions 1.9 cm and 54.6 cm on the scale. The voltage read by the DMM is 1.000 V and the current read the by DMM is 42mA. What is the resistance per unit length of the nichrome wire? (Does the DMM affect the resistance measurement?)
b)The accuracy of the multimeter is cited as ±0.7% ±1 digit on the voltage range and ±1% ±1 digit for the 300 mA range. What are the uncertainties of the voltage and current readings and the resultant uncertainty of the resistance of the wire?
2. a)Show that I(t) = (I_0)(e^(-t/RC)) solves the differential equation for the current through a discharging capacitor if I_0 = V_0/R, and t=0 is the time the discharging starts. Hint: Use Ohm's law, Kirchoff's laws and the identity de^(at)/dt = ae^(at)
b) Find the charge and voltage on the capacitor as a function of time.
1 a) Resistance per unit length = [1.000/(42*10^-3)]/(54.6 - 1.9) = 0.45 ohm cm^-1 DMM internal resistance is very high so it does not affect the resistance measurement.
b) Voltage as measured in A = 1.000 +/-0.007 and current = 42 +/-0.42
Corresponding uncertainty in resistance = 0.007+0.01 = 0.017 times resistance. So Resistance of the wire = 1000/42 = 23.82 +/-(23.82*0.017) = 23.8+/-0.4
2 a) By Kirchhoff laws we have
Q/C + IR = V or dQ/dt + (RC)*dI/dt = 0 or
dI/dt + (1/RC)*I = 0 or
dI/I = - dt/(RC) or ln I = -t/(RC) +C, when t = 0 I = V/R = Io say, this gives
I = Io*e^-[t/(RC)]
b) Vc = V - IR = IoR - IoR*e^-[t/(RC)] = V[1-e^-{t/(RC)}]
Q = CV[1-e^-{t/(RC)}] = Qo[1-e^-{t/(RC)}] where Qo is the maximum charge that capacitance can store for potential difference = V
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