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1301

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Physics

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Dec 6, 2023

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RC Circuits UTD physics - Spring 2023 1 PRE-LAB NAME:___________________________ Course & Section _________________________ Feel free to draft your answers in pencil but remember that the pre-lab to be given to your TA must be in pen. 1. How can you change the time constant if the capacitance of the circuit is fixed? _________________________________________________________________________ [1] 2. Initially, how large is Δ𝑉𝑉 ( 𝑡𝑡 ) Δ𝑉𝑉 ( 0 ) ? After an infinitely long time, what is the value of Δ𝑉𝑉 ( 𝑡𝑡 ) Δ𝑉𝑉 ( 0 ) ? ____________________________________________________________________________ _________________________________________________________________________ [2] 3. Find 𝑡𝑡 1 / 20 in terms of 𝜏𝜏 . Will 𝑡𝑡 1 / 20 be changed if the time constant for the circuit is increased? If it changes, explain how. ____________________________________________________________________________ ____________________________________________________________________________ _________________________________________________________________________ [2] 4. Now use Δ𝑉𝑉 ( 𝑡𝑡 ) Δ𝑉𝑉 ( 0 ) = 𝑒𝑒 − t 𝜏𝜏 to show that 𝑡𝑡 1 / 2 = 𝜏𝜏 ln2 . ____________________________________________________________________________ _________________________________________________________________________ [2] 5. What is the ratio of the voltage at 𝑡𝑡 = 20 𝜏𝜏 to the initial voltage across the capacitor? ___________________________________________________________________________ _________________________________________________________________________ [2] Since the ? = ??, if capacitance is fixed, to changing the resistance will change the time constant. Initially Δ()/Δ(0) = e^(-t/), if t=0 then Δ()/Δ(0) = e^(-0/) = 1. After an infinitely long time, Δ()/Δ(0) = e^(- ∞/?) = 0 When the time constant of a circuit is increased, it results in a proportional increase in the time taken for the circuit to reach a specific state or achieve a certain behavior. In other words, a longer time constant corresponds to a longer time duration for the circuit to respond or settle to a new condition. The ratio of the voltage at ? = 20? to the initial voltage across the capacitor is given by 1 - ??^( −20), where ? is the time constant of the RC circuit. The relationship Δ()/Δ(0) = e^(-t/) implies that 1/2, the time at which the voltage across the capacitor decreases to half of its initial value, is equal to ? times the natural logarithm of 2, or ?1/2 = ?ln2. NEEL BANSAL 2126.102

RC Circuits UTD physics - Spring 2023 2 6. How can the sum of voltages be a constant when 𝑽𝑽 𝑪𝑪 < 𝑽𝑽 𝑨𝑨 ? ____________________________________________________________________________ _________________________________________________________________________ [2] 7. Identify the parts of the cycle at which the current is smallest. _________________________________________________________________________ [1] 8. Calculate the approximate time constant for circuit one. _________________________________________________________________________ [1] 9. …what approximate frequency corresponds to T = 20 τ ? ___________________________________________________________________________ _________________________________________________________________________ [1] 10. Will this decay still be an exponential function of time? Will the time constant have changed? Explain. ____________________________________________________________________________ ____________________________________________________________________________ _________________________________________________________________________ [2] 11. Use the points selected to find the time constant; _________________________________________________________________________ [1] 12. Here is another decay: calculate the time constant using the points selected. _________________________________________________________________________ [1] In certain dynamic situations, such as during charging or discharging processes, or due to changes in circuit parameters or input conditions, the sum of voltages in a circuit can be a constant even when the voltage across a capacitor (VCC) is less than the voltage across an inductor (VLL). In an AC circuit with an inductive element, such as an inductor, the current is smallest at the points of the cycle where the voltage is at its peak due to the inductor's resistance to changes in current. These points, commonly referred to as "zero crossing" points, have the highest rate of change of voltage and result in the smallest current. Time constant = 0.002 sec .T=20*tau=20*0.002 =0.04 seconds then frequency=1/T=25 Hz The decay will still be exponential and time constant will also remain the same as R*C.only the time at which the curve starts changes.This will still be exponential, as it is exponential everywhere in the V-t graph.The time constant is still the same, as it follows the same shape. The time constant is τ=4.2099 ∗10−2 s−4.0348∗10 −2 s=0.1751∗10−2 s =8.1478 ∗10−2s−8.0262∗10−2s=0.1216∗10−2s

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