Question

In the figure below, R_1 = 0.335 Ohm, R_2 = 3.35 Ohm, and R_3 = 33.5 Ohm. Find the equivalent resistance of the circuit and the current in each resistor when a 7.00-V is connected between points A and B, points A and C, and points A and D. (a) points A and B R_eq = Ohm IR_1 = A IR_2 A IR_3 = A I_100 = A b) points A and C R_eq= Ohm IR_1 = A IR_2 A IR_3 = A I_100 = A (c) points A and D R_eq = Ohm IR_1 = A IR_2 A IR_3 = A I_100 = A

Answer 1

(a ) ans

the 100ohms , R2 and R3 are in series connection

the resistance R=100+R2+R3=100+3.35+33.5=136.9 ohms

now the resistance R and R1 are parallel connection

the effecitive resistance R"=136.9*0.335/136.9+0.335

=0.3342 ohms..................................(1)

the current at resistance R1=>I1=V/R1=7/0.335=20.9 A

the potential difference at resistance R2=>V2=7*3.35/100+3.35+33.5

=0.2 v

the current at resistance R2=>I2=0.2/3.35=0.1 A

the potential difference at resistance R3=>V3=7*33.5/136.85=1.714 v

the current at resistance I4=1.714/33.5=0.1 A

the potential difference at 100 ohms resistance =>V4=7*100/100+3.35+33.5=5.12 v

thr current at 100 ohms resistance =>I4=V4/R4=5.12/100=0.0512=0.1 A

(b) ans

the resistance R3 and 100 ohms are series connection

resistance R'=33.5+100=133.5 ohms

the resistance R2 and R1 are series connction

resistance R"=0.335+3.35=3.685 ohms

the resistance R" and R' are parallel connection

the effective resistance =3.685*133.5/133.5+3.685=491.95/137.185

=3.59 ohms

the potential difference at resistance R1=>V1=7*0.335/3.35+0.335=0.64 v

the current at resistance R1=>I1=0.64/0.335=1.91 A

the potential difference at resistance R2=>V2=7*3.35/3.685=6.4 v

the current at resistance R2=>I2=6.4/3.35=1.91 A

the potential difference at resistance R3=>V3=7*33.5/133.5=1.76 v

the current at resistance R3=>I3=1.76/33.5=0.1 A

the potential difference at resistance 100 ohms =>V4=100*7/133.5=5.24 v

the current at resistance 100 ohms =>I4=5.24/100=0.1 A

(c) ans

the resistance R1,R2 and R3 are series connection

resistance R'=0.335+3.35+33.5=37.185 ohms

now resistance R' and 100 ohms are in parallel

the effective resistance R"=100*37.185/100+37.185=27.11 ohms

now the current at 100 ohms resistance =>I4=7/100=0.1 A

the potential difference at resistance R1=>v1=7*0.335/37.185=0.0631 V

the current at resistance R1=>I1=0.0631/0.335=0.19 A

the potentail difference at resistance R2=>V2=7*3.35/37.185=0.631 v

the currenrt at resistance R2=>I2=0.631/37.185=0.02 A

the potential difference at resistance R3=>V3=7*33.5/37.185=6.31 v

the current at resistance R3=>I3=6.31/33.5=0.17 A