Chapter 28: Q. 35 (page 792)

A $10 μ F$ capacitor initially charged to $20 μ C$ is discharged through a $1.0 k Ω$ resistor. How long does it take to reduce the capacitor’s charge to $10 μ C$ ?

Short Answer

Expert verified

$t = 6.9 m s$ time will be taken to reduce the cpacitor's charge to $10 μ C$ .

Step by step solution

Given Information

We need to find that how long does it take to reduce the capacitor’s charge to $10 μ C$ .

Simplify

The switch is off, the capacitor discharge and the current flows through the resistor. To discharge the capacitor, the charges flow through the circuit in time $r$ . The initial charge $Q_{o}$ is related to the final charge $Q$ by equation in the form

$Q = Q_{o} e^{\frac{- t}{R C}}$ (1)

Here, $R$ is the resistance and $C$ is the capacitance. Let us solve equation (1) to get it by

$t = - R C I n (\frac{Q}{Q_{o}})$ (2)

Now, putting the values for $R, C, Q$ and $Q_{o}$ into equation (2) to get $t$

$t = - R C I n (\frac{Q}{Q_{o}}) = - (1000) (10 \times 10^{- 6} F) I n (\frac{10 μ C}{20 μ C}) = 6.9 \times 10^{- 3} s = 6.9 m s$

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A $10 μ F$ capacitor initially charged to $20 μ C$ is discharged through a $1.0 k Ω$ resistor. How long does it take to reduce the capacitor’s charge to $10 μ C$ ?

Short Answer

Step by step solution

Given Information

Simplify

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A 10μFcapacitor initially charged to 20μCis discharged through a 1.0kΩ resistor. How long does it take to reduce the capacitor’s charge to 10μC?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

A $10 μ F$ capacitor initially charged to $20 μ C$ is discharged through a $1.0 k Ω$ resistor. How long does it take to reduce the capacitor’s charge to $10 μ C$ ?