For the alarm circuit of Figure 11-32, the input from the sensor is 5 V, C= 47 μF, and the alar

step 1 For Part A, in normal operation, the capacitor is fully charged by the power supply. And so the

For the alarm circuit of Figure 11-32, the input from the...

For the alarm circuit of Figure 11-32, the input from the sensor is $5 \mathrm{~V}, C=$ $47 \mu \mathrm{F}$, and the alarm is activated when $v_C=4.2 \mathrm{~V}$. Choose the nearest standard resistor value to achieve a delay of at least $37 \mathrm{~s}$.
(FIGURE CAN'T COPY)

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Key Concepts

Standard Resistor Values

Resistors are manufactured in standard values following series such as the E-series. When calculated resistance values do not match a standard value exactly, the nearest standard resistor is chosen to ensure practical implementation and component availability in circuit design.

Exponential Charging Equation

The voltage across a charging capacitor follows an exponential behavior described by the equation V(t) = V_supply × (1 - e^(-t/RC)). This equation is essential for determining the time required to reach a specific voltage threshold, which is crucial in applications like timed alarms and delays.

Time Constant

The time constant, denoted as ? (tau) and calculated as the product of resistance (R) and capacitance (C), represents the time it takes for the capacitor to charge to about 63% of its final voltage in a charging circuit. It is a critical parameter in designing circuits that require a specific delay.

RC Circuits

An RC circuit is composed of a resistor and a capacitor, and it is widely used in timing and delay applications. The capacitor charges or discharges through the resistor, and the rate of this process defines the timing characteristic of the circuit.

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