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.
Answers
Given : 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.
To Find :
(a) the equivalent resistance
(b) 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)Power output of the source and show that it equals the total power dissipated by the resistors.
Solution:
Connected in Parallel
Hence
1/R = 1/R₁ + 1/R₂ + 1/R₃
=> 1/R = 1/1 + 1/2 + 1/2
=> 1/R = 2
=> R = 1/2
the equivalent resistance = 1/2 Ω
I = V/R
= 3/(1/2)
= 6A
Current supplied by the source to the parallel circuit. is 6A
currents in each resistor
3/1 = 3A
3/2 = 1.5A
3/2 = 1.5A
3 + 1.5 + 1.5 = 6A
power dissipated by each resistor = I²R
3²(1) = 9 W
(1.5)²(2) =4.5 W
(1.5)²(2) = 4.5 W
Power output at source = (6)²(1/2) = 18W
9 + 4.5 + 4.5 = 18W
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