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Chapter 4: Q46E (page 876)

A 1.50- μF capacitor is charging through a 12.0-Ω resistor using a 10.0-V battery. What will be the current when the capacitor has acquired14of its maximum charge? Will it be14of the maximum current?

Short Answer

Expert verified

When the capacitor has acquired14 of its maximum charge then the current will be 0.625 A

Step by step solution

01

Relation between Resistance and capacitance

Resistance and capacitance are related in the manner that resistance affects directly the time taken to charge a capacitor. Or we can also say that as resistance increases the time taken to charge the capacitor also increases.

02

Calculating the current

We know that the current in the circuit when the capacitor is 14of the maximum, we can calculate the exponential term:

Q=Qmax4Q=Qmax4Q=Qmax1-e-tRC-e-tRC=34

We can finally calculate the current:

I=Imaxe-1RC=Imax34=VR×34=10.0V12.0Ω×34=0.625A

Therefore the current is 0.625 A.

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