Question

Find the current through resistor R_1 and the voltage across resistor R_4.

Answer 1

here,

Since r4 and r3 are in sereis so,
r' = 220 + 680 = 900 ohms

now this r' will be in parallel with r2
r'' = r' * r2/(r' + r2)
r'' = 900 * 1000 (1000 + 900)
r'' = 1710000000 ohms

now this r'' will be in series with r1 so eqivalent resistance will be :
req = r1 + r''
req = 680 + 1710000000
req = 1710000680 ohms

From ohm's Law total current in circuit will be :
I = v/req
I = 12 / 1710000680
I = 7.018*10^-9 A

Current Through R1 = Total current in circuit.
I1 = 7.018*10^-9 A

Since voltage remain same across resistor in parallel so,
V4 = V * R4 /(r')
V4 = 12 * 680/(900)
V4 = 9.067 v