Find the potential difference across each resistor in the fi

Find the potential difference across each resistor in the figure below. (R1 = 5.20 , R2 = 3.80 , R3 = 2.60 , R4 = 1.60 ) V1 = V V2 = V V3 = V V4 = V

Having issues solving part B) for this question as well...

A charged capacitor is connected to a resistor and switch as in the figure below. The circuit has a time constant of 1.60 s. Soon after the switch is closed, the charge on the capacitor is 50.0% of its initial charge.

(a) Find the time interval required for the capacitor to reach this charge.
1.11 s

(b) If R = 290 k, what is the value of C?

Solution

current throught battery 12V is i1 upward, through 3V is i2 upward and through 18V is i3 upward.

- i1R1 + 12 - 3 + i2R2 = 0

5.20i1 - 3.80i2 = 9 ............. (i)

in right side loop:

- i3 R4 + 18 - 3 + i2R2 - i3R3 = 0

-3.80i2 + 4.2i3 = 15 .... (ii)

Applying KCL: i1 + i2 + i3 = 0 ..... (iii)

solving three equations,

i1 = 125/448 = 0.282 A

i2 = -445/224 = 2 A

i3 = 765/448 = 1.708 A

V1 = i1R1 = 0.282 x 5.20 = 1.46 Volt

V2 = 2 x 3.80 = 7.6 Volt

V3 = 1.708 x 2.60 = 4.44 Volt

V4 = 1.708 x 1.60 =2.73 Volt

-------------------------------

(B) time constant = R C

1.60   = (290 x 10^3) (C)

C = 5.52 x 10^-6 F   Or 5.52 uF