The circuit shown in Figure P11.62 can be used as a timer...

The circuit shown in Figure P11.62 can be used as a timer circuit. Switch $S_1$ is closed at $t=0$ and the capacitor is initially uncharged; at time $t_1$ the thyristor will fire and turn on the small indicator light, which has a resistance of $100 \Omega$. The thyristor has $V_{B O}=20 \mathrm{~V}$ and $I_H=30 \mathrm{~mA}$. Find time $t_1$. Figure P11.62 can't copy

Key Concepts

Thyristor Operation and Triggering

Thyristor operation involves the device switching from a non-conducting state to a conducting state when its gate receives a sufficient triggering current and the voltage across it exceeds a certain level. This concept ties together the requirement of a minimum current and voltage for the thyristor to fire, making it central to timing and switching applications.

Threshold Triggering in Nonlinear Devices

Threshold triggering refers to the condition where a nonlinear device, such as a thyristor, is activated once the voltage or current in the circuit reaches a certain preset level. Understanding these conditions is crucial in timing circuits where precise activation, such as firing a thyristor, is required.

RC Time Constant

The RC time constant, represented by the product of resistance (R) and capacitance (C), is a key concept in circuits involving a resistor and capacitor. It determines how quickly the capacitor charges or discharges and is essential for predicting the timing behavior of the circuit.

Capacitor Charging Dynamics

Capacitor charging is the process by which a capacitor accumulates voltage over time when connected to a power source through a resistor. The voltage across the capacitor increases exponentially towards the supply voltage according to the equation V(t) = V_source × (1 - e^(-t/RC)), making it an important concept in any timing circuit.

Exponential Voltage Build-Up

The exponential build-up of voltage across a capacitor in an RC circuit describes how the voltage asymptotically approaches a final value over time. This mathematical behavior is critical for calculating the time at which the voltage reaches specific threshold values required to trigger subsequent circuit actions.

Transcript

00:01 In this question, we have a simplified circuit for a photographic flash unit.

00:07 The circuit consists of a battery, a resistor, and a capacitor, whose values we are aware of, as well as two switches.

00:17 We are asked to calculate the time it takes for the capacitor to charge to a voltage of five volts once the first switch is closed.

00:31 Now, we do have a formula for this type of circuit.

00:34 Once switch one is closed, we have a very typical rc circuit, and we do have a formula for the charge on the capacitor as a function of time.

00:51 But in order to use this formula to get at the time that we're interested in, we're going to need to know what the charge is, the corresponding charge is at that time.

01:00 Now, we know that the capacitance is 140 microferods, and we also know that we want that to be charged to a voltage of 5 volts at the time that we're considering.

01:15 So what we can do is take the capacitance and the voltage and calculate the corresponding charge.

01:22 So the charge on the capacitor at the time we're interested in is going to be c times v, 140.

01:34 Microfarads times five volts.

01:38 And so that's gonna give us a value of 700 microculems.

01:44 So basically this problem is equivalent to asking how long does it take for the capacitor to be charged to a charge of 700 microculems? so we're just gonna take that formula that we have for this and seven the values that we have.

02:04 So the capacitance is 140 micro ferats.

02:11 The emf or the voltage on the battery is 9 volts.

02:19 And then we have 1 minus e to the minus t over tau.

02:25 Now, tau is the time constant.

02:28 That's going to be r times c.

02:30 So let's just do a quick calculation of that on the side...

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