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Chapter 27: Q96P (page 802)

Figure 27-63 shows an ideal battery of emf e= 12V, a resistor of resistanceR=4.0惟,and an uncharged capacitor of capacitance C=4.0渭贵 . After switch S is closed, what is the current through the resistor when the charge on the capacitor 8.0渭颁?

Short Answer

Expert verified

The current through the resistor when the charge on the capacitor 8.0渭C is I=2.50A .

Step by step solution

01

Write the given quantities

e=12VR=4.0惟C=4.0渭Fq=8.0渭C

02

Determine the concept of capacitance and Ohm’s law  

Voltage across capacitance depends on charge and capacitance. According to Ohm鈥檚 law, current is directly proportional to potential difference across a circuit's ends.

Formulae:

Voltage across capacitance C is as follows:

VC=qC

Current across resistance R is as follows:
role="math" localid="1662365364559" iR=VRR

03

Determine the value of current through the capacitance: 

Voltage across capacitance C is .

Vc=8脳10-64脳10-6

Voltage across R is VR = e - Vc.

VR= 12-2

=10V

Hence, current through resistance R

iR=VRR

Substitute the values and solve as:

iR=104=2.50A

The current through the resistor when the charge on the capacitor 8.0渭Cis I=2.50A

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Most popular questions from this chapter

A 10-km-long underground cable extends east to west and consists of two parallel wires, each of which has resistance 13 鈩�/km. An electrical short develops at distance xfrom the west end when a conducting path of resistance Rconnects the wires (Figure). The resistance of the wires and the short is then 100 鈩� when measured from the east end and 200 鈩� when measured from the west end. What are

(a) xand

(b) R?

In Fig. 27-58, a voltmeter of resistance RV=300惟and an ammeter of resistanceRA=3.00惟 are being used to measure a resistance R in a circuit that also contains a resistance R0=100惟and an ideal battery with an emf of 蔚=12.0V. ResistanceR is given by R=V/i, whereV is the potential across Rand iis the ammeter reading. The voltmeter reading is V', which is V plus the potential difference across the ammeter. Thus, the ratio of the two-meter readings is not R but only an apparent resistance role="math" localid="1664348614854" R'=V/i. If R=85.0惟, what are (a) the ammeter reading, (b) the voltmeter reading, and (c)R' ? (d) IfRA is decreased, does the difference betweenR' andR increase, decrease, or remain the same?

Figure 27-78 shows a portion of a circuit through which there is a current I=6.00A. The resistances are R1.=R2=2.00R3=2.OOR4=4.00惟What is the currenti1through resistor 1?

In Fig. 27-55a, resistor 3 is a variable resistor and the ideal battery has emf.蔚=12V Figure 27-55b gives the current I through the battery as a function of R3. The horizontal scale is set by.R3s=20惟The curve has an asymptote of2.0鈥尘础asR3鈫�鈭�. What are (a) resistanceR1and (b) resistance R2?

Initially, a single resistorR1 is wired to a battery. Then resistor R2is added in parallel. Are

(a) the potential difference across R1and

(b) the currenti1 through R1now more than, less than, or the same as previously?

(c) Is the equivalent resistance R12of R1and R2more than, less than, or equal toR1 ?

(d) Is the total current through R1andR2together more than, less than, or equal to the current through R1previously?
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