Five 4.0 Ω resistors are connected in parallel to a 20.0-V battery. What is the current in any one of the resistors?
First you have to find the total resistance of the five 4.0Ω resistors.
Let's 'pair' up the resistors and figure it out...
Resistor A (4Ω) in parallel with Resistor B (4Ω) equals 2Ω. (Resistor AB)
Resistor C (4Ω) in parallel with Resistor D (4Ω) equals 2Ω. (Resistor CD)
Resistor AB (2Ω) in parallel with Resistor CD (2Ω) equals 1Ω (Resistor ABCD).
Now we have a 1Ω resistor (ABCD) in parallel with a 4Ω resistor (E)
R(total) = (1 * 4) / (1 + 4) = 4/5Ω or 0.8Ω
The *total* current is 20V / 0.8Ω = 25 amps.
25 amps divided into five parallel resistors equals (you crunch the numbers).
Best of luck in your studies,
~ Mitch ~
.
I = V/R
The voltage across any one resistor is 20V
I = 20/4 = 5A
m07232012
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Verified answer
First you have to find the total resistance of the five 4.0Ω resistors.
Let's 'pair' up the resistors and figure it out...
Resistor A (4Ω) in parallel with Resistor B (4Ω) equals 2Ω. (Resistor AB)
Resistor C (4Ω) in parallel with Resistor D (4Ω) equals 2Ω. (Resistor CD)
Resistor AB (2Ω) in parallel with Resistor CD (2Ω) equals 1Ω (Resistor ABCD).
Now we have a 1Ω resistor (ABCD) in parallel with a 4Ω resistor (E)
R(total) = (1 * 4) / (1 + 4) = 4/5Ω or 0.8Ω
The *total* current is 20V / 0.8Ω = 25 amps.
25 amps divided into five parallel resistors equals (you crunch the numbers).
Best of luck in your studies,
~ Mitch ~
.
I = V/R
The voltage across any one resistor is 20V
I = 20/4 = 5A
m07232012