Question

Find i(t) for t > 0 in the circuit below.

2kΩ 2kΩ 1kΩ - ΑΛΛ- + 12V 4kΩ + 100μF t=0 i(t)

Answer 1

Given circuit is 2Kn 2KO MWV IKR WWW mw K 12 V - 4K 2 Vit). t=o ict) 100HF I If you observe for it to) there is Source acting on Then Capacitor absence of Voltage across Capacitor v (t) is given by -tk Vict) vo.e Initial voltage acrorr capacitor (or) Voltage across capacitor under steady State before Switch operation T = Time Constant REQ Cual

for V (to) IK 2k12 2KR WWW www MW EARR + 12V loop 3 KvL loop Eq" ; - 12 + 1 (1+2+2+4)X10 <3 xlo 1.33 mA I = 124 93 ✓ 1 ( 6x1B) = (1-23 x 10") (6x109) 7.98 v for a (txo) 2KR 2K2 WWW w we 1K2 ( Redundant) Suka b Rab وه (6K) II (26) (6K) (26) 11 12 k = (1.5x103) 82 (6+2)k Cab Eq ( 100 <10%) (0.1x10²) F T = Rab Cab (1-5*10) (0-1x103) = 0.15 -15 Now; voltage across Capacitor yct) 7.98 e

2KO MUM ilt) UK2 www Yct) KIL ; loop - VCE) + ilt) ((1+2)x18) i(t) (t) 6x103 -t/.15 7.98 e 6x103 - loot 15 10 ilt) (1-33 - loot 15 (1.33 e x103) & i(t)
Thank You.