Question

Three resistors R1=1.00Ω , R2=2.00Ω , and R3=2.00Ω , are connected in parallel. The parallel connection is attached to a V=3.00V voltage source. (a) What is the equivalent resistance? (b) Find the current supplied by the source to the parallel circuit. (c) Calculate the currents in each resistor and show that these add together to equal the current output of the source. (d) Calculate the power dissipated by each resistor. (e) Find the power output of the source and show that it equals the total power dissipated by the resistors.

Answer 1

given,

r1 = 1ohm

r2 = 2ohm

r3 = 2ohm

are connected in parallel to 3V source.

(a) equivalent resistance,

1/r(eq.) = 1/r1 + 1/r2 +1/r3

= 1/1 + 1/2 + 1/2

= 2

so, r(eq.) = 1/2 ohm.

(b) we know,

V = IR

3 = I*1/2

I = 6A

(c) I = V/R

I(in r1) = 3/1 = 3A

I(in r2) = 3/2 = 1.5A

I(in r3) = 3/2 = 1.5A

Total current supplied = 3A + 1.5A + 1.5A

= 6A.

(d) Power = V I = V^2/R

(In r1); Power = (3)^2/r1 = 9/1 = 9 watt

(In r2); Power = (3)^2/r2 = 9/2 = 4.5 watt

(In r3); Powrr = 9/r3 = 9/2 = 4.5 watt

(e) Power(total) = V I

= 3*6 = 18 watt

Sum of Power in(r1,r2,r3) = 9 + 4.5 + 4.5 = 18 watt

Which is equal total power.