What is the current throught resistor a when switch A and B

What is the current throught resistor a, when switch A and B have been open for a long time? 0 A 5 A 9 A 10 A What is the current through resistor a when switch A and B have been open for a long time? 0 A 5 A 9 A 10 A

Solution

When switch A is closed for long d and f are in parallel and effective resisance of d and f = 2 ohms

combined (d,f) and g are in series effective resistance is = 2+2 = 4 ohms

this combination of d,f,g is ina parallel with c (12 ohms )

effective ressitance of the combination = 3 ohms

Now we have 90 V connected to 4+2+3 ohms in series

potential across 3 ohms = 90 *3/9   = 30 V

Potential across g = 30/2 = 15V

The capacitor will be charged to 15 V

energy in the capacitoe = (1/2)CV² = 1.0e-6 *15² = 1.125e-4 J   - 5(a)

The capacitor is charged to 15 V - 6(e)

7. when A is closed and B is open

90 V is connected to 4+2+12 ohms

current = 90 /18 = 5A   ---(b)

8. when B is closed and A is open g(4) and f(2) are in series and in paralle with c(12)

effective resistance = 4 ohms

90 V connected to 4+2+4 ohms

current   = 90/10 = 9 A   -- (c)

9. Above curent 9 a is shared through c(12) and g,f combination 6 ohms

current through g,f is more as the resistance is more   = 9*2/3   = 6A --- (b)

10. remaining current 3A would flow through c(12)   = 3A --- (a)