College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

The given pair of capacitors in Figure P18.67 is fully charged by a 12.0-V battery. The battery is disconnected and the circuit closed. After 1.00 ms, how much charge remains on (a) the 3.00-μF capacitor? (b) The 2.00-μF capacitor? (c) What is the current in the resistor?Figure P18.67

(a)

To determine

The current in the 4.00V battery from the given circuit.

Explanation

Given Info: Apply the Kirchhoffâ€™s junction rule and loop rule to the loop â€˜gbcfgâ€™ and â€˜fcdefâ€™

Apply the junction rule at the point c in the given figure we get,

â€‚Â I1=I3âˆ’I2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (1)

• I1, I2 and I3 is the current in the given circuit,

Apply kirchoffâ€™s loop rule to the loop gbcfg.

â€‚Â 8.00â€‰V+3.00I2âˆ’5.00I1=0

Rewrite the above relation,

â€‚Â 5.00I1âˆ’3.00I2=8.00â€‰VÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (2)

Again apply kirchoffâ€™s loop rule to the loop fcdef we get,

â€‚Â âˆ’3.00I2âˆ’5.00I3+4.00â€‰V=0

Rewrite the above relation,

â€‚Â 5.00I3+3.00I2=4.00â€‰VÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (3)

Substitute equation (1) into equation (2) will get,

â€‚Â I1=I3âˆ’I25

(b)

To determine

The current in the 3.00Ω resistor.

(c)

To determine

The current passing through the 8.00 V batteries.

(d)

To determine

The current passing through the 3.00 V batteries.

(e)

To determine

The charge on the capacitor.

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