   Chapter 18, Problem 56AP

Chapter
Section
Textbook Problem

An emf of 10 V is connected to a series RC circuit consisting of a resistor of 2.0 × 106 Ω and an initially uncharged capacitor of 3.0 μF. Find the time required for the charge on the capacitor to reach 90% of its final value.

To determine
The power consumed by the series configuration is 1/n2 times the power consumed by the parallel configuration.

Explanation

Given Info: The resistance of the resistor is R and the applied voltage is ΔV . The resistance of the resistor is R and the applied voltage is ΔV .

Explanation:

Formula to calculate the equivalent resistance of the resistor connected in series is,

Requ=R1+R2+.........+nR

• Requ is the equivalent resistance of the resistor in series combination,
• R1 , and R2 is the resistors
• nR is the number of resistors,

The current passing through equivalent resistance of the resistor connected in series is,

Is=ΔVRequ (1)

• Is is the current passing through equivalent resistance,
• ΔV is the applied voltage in series configuration of n resistors,

Use nR for Requ in equation (1).

Is=ΔVnR

The power consumed by the series configuration is,

Ps=Is2Requ

• Ps is the power consumption in series configuration,

Use ΔV/nR for Is and nR for Requ in above relation.

Ps=(ΔV)2(nR)2(nR)=(ΔV)2nR (2)

Thus, the power consumed by the series configuration of n resistors is Ps=(ΔV)2/nR

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