Question

A two-resistor voltage divider employing a 2-k and a 3-k resistor is connected to a 5-V ground-referenced power supply to provide a 2-V voltage. Sketch the circuit. Assuming exact-valued resistors, what output voltage (measured to ground) and equivalent output resistance result? If the resistors used are not ideal but have a ±5% manufacturing tolerance, what are the extreme output voltages and resistances that can result?

Answer 1

A two-resistor voltage divider circuit, with a 2-kΩ and a 3-kΩ resistor connected in series, is used to obtain a 2-V output voltage from a 5-V power supply. The output voltage can be calculated using the voltage divider formula, and the equivalent output resistance is the sum of the resistances of the two resistors.

Step-by-step explanation:

A voltage divider circuit is used to divide the input voltage into a desired output voltage using resistors. In this case, a 2-kΩ and a 3-kΩ resistor are connected in series, and the circuit is connected to a 5-V power supply. The output voltage is 2 V.

The output voltage can be calculated using the voltage divider formula:

Vout = Vin * (R2 / (R1 + R2))

The equivalent output resistance can be calculated as the total resistance of the series resistors:

Req = R1 + R2 = 2 kΩ + 3 kΩ = 5 kΩ

Considering the ±5% manufacturing tolerance of the resistors, the extreme output voltages can be calculated as follows:

Vout_min = Vin * (R2_min / (R1_max + R2_min))

Vout_max = Vin * (R2_max / (R1_min + R2_max))

The extreme output resistances can be calculated as:

Req_min = R1_max + R2_max

Req_max = R1_min + R2_min

Answer 2

Rout=1.2K

Vmax=2.12V; Vmin=1.88V

Rmax=1.26K

Rmin=1.14K

Step-by-step explanation:

You can find the circuit diagram attached.

Seing from the output and with no power supply, the output resistance will be R1 in parallel to R2:

Rout = R1 // R2 = 1.2K

The maximum output voltage will be when R1 = 3K-5% and R2 = 2K+5%:

`Vmax = (2.1K)/(2.1K + 2.85K) *5V=2.12V`

Minimum voltage will be when R1 = 3K+5% and R2 = 2K-5%:

`Vmin = (1.9K)/(1.9K + 3.15K) *5V=1.88V`

As for the output resistance:

Rmax will be when R1 = 3K+5% and R2 = 2K+5%:

Rmax = 1.26K

And Rmin will be when R1 = 3K-5% and R2 = 2K-5%:

Rmax = 1.14K