A resistor rated at 690 kΩ is connected across two D cell batteries (each 1.50 V) in series, with a total voltage of 3.00 V. The manufacturer advertises that their resistors are within 4% of the rated value. What are the possible minimum current and maximum current through the resistor (in µA)?

Respuesta :

Answer:

The possible minimum current and maximum current through the resistor is 4.53 μA and 4.18 μA

Explanation:

Given that,

Resistance = 690 kΩ

Total voltage = 3.00 V

We need to calculate the maximum resistance

[tex]R_{max}=690000+(\dfrac{4}{100}\times690000)[/tex]

[tex]R_{max}=717600\ \Omega[/tex]

We need to calculate the minimum resistance

[tex]R_{min}=690000-(\dfrac{4}{100}\times690000)[/tex]

[tex]R_{min}=662400\ \Omega[/tex]

We need to calculate the maximum and minimum current

Using ohm's law

For maximum current,

[tex]V = I R[/tex]

[tex]I_{max}=\dfrac{V}{R_{max}}[/tex]

[tex]I_{max}=\dfrac{3.00}{717600}[/tex]

[tex]I_{max}=0.00000418\ A[/tex]

[tex]I_{max}=4.18\times10^{-6}=4.18\ \mu A[/tex]

For minimum current,

[tex]I_{max}=\dfrac{3.00}{662400}[/tex]

[tex]I_{min}=0.00000453\ A[/tex]

[tex]I_{min}=4.53\times10^{-6}= 4.53\ \mu A[/tex]

Hence, The possible minimum current and maximum current through the resistor is 4.53 μA and 4.18 μA

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