Question

Real resistors can only be manufactured to a specific tolerance, so that in effect the value of the resistance is uncertain. For example, a 1Ω resistor specified as 5% tolerance could in practice be found to have a value anywhere in the range of 0.95 to 1.05Ω. Calculate the potential voltage range across a 2.2 kΩ 10% tolerance resistor if the current flowing through the element is 4 sin 44t mA.

Answer 1

The potential voltage range across a 2.2 kΩ 10% tolerance resistor when current of 4 sin 44t mA is flowing through the element is between a range of 7.92sin44t and 9.68sin44t volts.

Step-by-step explanation:

Given that there is 10% tolerance for the 2.2 kΩ resistor, this implies that the resistance would range between 2,200 — 10% of 2,200 and 2,200 + 10% of 2,200, which is:

(i) 2,200 — 10% of 2,200 = 2,200 — 220 = 1,980 Ω, and

(ii) 2,200 + 10% of 2,200 = 2,200 + 220 = 2,420 Ω

Therefore, we will calculate the potential voltage for 1,980 Ω and 2,420 Ω if the current flowing through the element is 4sin44t mA:

(a) The potential voltage for a resistance of 1,980 Ω: we will use the formula: potential voltage v = i × R

Where i = 4sin44t mA = 0.004sin44t A, and R = 1,980 Ω

The potential voltage = v = 1,980 × 0.004sin44t = 7.92sin44t (in volts)

(b) The potential voltage for a resistance of 2,420 Ω: we will use the formula: potential voltage v = i × R

Where i = 4sin44t mA = 0.004sin44t A, and R = 2,420 Ω

The potential voltage = v = 2,420 × 0.004sin44t = 9.68sin44t (in volts)