Use the technique of simplifying this circuit using equivale

Use the technique of simplifying this circuit using equivalent resistances into smaller, simpler circuits. Given the following circuit: If R1 = 36 Ohm, R_2 = 20 Ohm, R_3 = .30 Ohm, and V_s = 12 Volts, determine the circuit equivalent resistance (REQ) and the circuit current (I). Also calculate the branch currents through R2 and R3, and the voltage drops across R1, R2, and R3.

Solution

R2 & R3 are parallel so : 1/R =1/R2 + 1/R3 => R_parallel=(20*30)/(20+30) =12 ohm

R1 & R are in series: so 12+36 =48 ohm.

Equivalent Resistance R_eq = 48 ohm

Current I =V/R= 12/48= 0.25A

Voltage Drop across R1=I*R1= 0.25 *36=9V

Voltage drop across R2 & R3 = I * R_parallel = 0.25* 12=3 V

Current in R3 = V_parallel/ R3 = 3/30=0.1 A

Current in R2= 0.25-0.1=0.15A