Question

Figure 25-33 shows a circuit section of four air-filled capacitors that is connected to a larger circuit. The graph below the section shows the electric potential V(x) as a function of position x along the lower part of the section, through capacitor 4. Similarly, the graph above the section shows the electric potential V(x) as a function of position x along the upper part of the section, through capacitors 1, 2, and 3. Capacitor 3 has a capacitance of 0.69 μF. What are the capacitances of (a) capacitor 1 and (b) capacitor 2?

Answer 1

( a )

potential across 4 = potential across ( 1, 2 , 3 ) ;

12 = 2 + 5 + V3 ;

V3 = 5 V ,

Q3 = C3 V3 = 0.69 e -6 * 5 = 3.45 e -6 C ;

Q3 = Q2 = Q1 = Q = 3.45 e -6 C ;

so

C1 = Q / V1 = 3.45 e -6 / 2 = 1.725 e -6 F = 1.725 μF ; <---------ans for 1

C2 = Q / V2 = 3.45 e -6 / 5 = 6.9 e -7 = 0.69 μ F <------ans for 2 ,