Chapter 4: Q48E (page 876)

A 1.50- $μ$ F capacitor is charging through a 12.0-Ω resistor using a 10.0-V battery. What will be the current when the capacitor has acquired $\frac{1}{4}$ of its maximum charge? Will it be $\frac{1}{4}$ of the maximum current?

Short Answer

Expert verified

When the capacitor has acquired $\frac{1}{4}$ of its maximum charge then the current will be 0.625A

Step by step solution

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 time taken to charge the capacitor also increases.

Calculating the current

We know that the current in the circuit when the capacitor is ¼ maximum, we can calculate the exponential term:

$Q = \frac{Q_{m a x}}{4} Q = \frac{Q_{m a x}}{4} = Q_{m a x} (1 - e^{\frac{- t}{R C -}}) e^{\frac{- t}{R C -}} = \frac{3}{4}$

We can finally calculate the current:

$l = l_{m a x} e^{\frac{- t}{R C}} = l_{m a x} (\frac{3}{4}) = \frac{V}{R} \frac{3}{4} = \frac{10.0 V}{12.0 Ω} \frac{3}{4} = 0.625 A$

Therefor the current is 0.625 A .

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A 1.50- $μ$ F capacitor is charging through a 12.0-Ω resistor using a 10.0-V battery. What will be the current when the capacitor has acquired $\frac{1}{4}$ of its maximum charge? Will it be $\frac{1}{4}$ of the maximum current?

Short Answer

Step by step solution

Relation between Resistance and capacitance

Calculating the current

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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 be 14of the maximum current?

Short Answer

Step by step solution

Relation between Resistance and capacitance

Calculating the current

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Rotational Dynamics

Measurements

Kinematics Physics

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Electrostatics

Study anywhere. Anytime. Across all devices.

A 1.50- $μ$ F capacitor is charging through a 12.0-Ω resistor using a 10.0-V battery. What will be the current when the capacitor has acquired $\frac{1}{4}$ of its maximum charge? Will it be $\frac{1}{4}$ of the maximum current?