Question

In the figure below. E = 9.00 V, R_1 = 100 Ohm, R_2 = 500 Ohm, and R_3 = 700 Ohm. (a) What is the equivalent resistance of the three resistors? (b) What is the electric potential across resistance 1? (c) What is the current through resistance 3?

Answer 1

(a) R2 and R3 are in parallel, so R23= (1/R2 +1/R3)^-1.

R23=(1/500 +1/700)^-1.

R23=291.67 ohm

R23 and R1 are in series, so the total equivalence resistance of the circuit= Rtotal= R23 + R1

Rtotal= 291.67 + 100

Rtotal= 391.67 ohm.

(b) total current= i= V/Rtotal

i= 9/391.67

i=0.023 A

current through R1 = i=0.023 A

so potential difference across R1 ig given by, V1= i R1

V1= (0.023)(100)

V1=2.3 volts.

(3)voltage across R2 and R3 is same and isgiven by

V2= v3= V- v1

V3= 9-2.3

V3=6.7 volts

so i3= V3/R3

i3= 6.7/700

i3=0.00957A