Two resistors of resistances 3 ohms and 6 ohms are connected in a parallel across a 9 V battery. What is the equivalent resistance and the total current in the circuit?
current through 3 ohms = 9/3 = 3 amps
current through 6 ohms = 9/6 = 1.5 amps
so
total current = 4.5 amps
equivalent R =V/i = 9/4.5 = 2 Ohms
or of course
1/R = 1/3+1/6 = 3/6
so R = 6/3 = 2
R=2ohms
I=v/R=9/2
I=4.5A therefore, i agree to bobpursley's answer
To find the equivalent resistance of resistors connected in parallel, you can use the formula:
1/Req = 1/R1 + 1/R2 + 1/R3 + ...
In this case, we have two resistors connected in parallel with resistances of 3 ohms and 6 ohms. Let's call the equivalent resistance Req.
1/Req = 1/3 + 1/6
Now, let's simplify this equation:
1/Req = (2 + 1)/6
1/Req = 3/6
1/Req = 1/2
To find Req, we need to find the reciprocal of both sides:
Req = 2 ohms
So, the equivalent resistance of the two resistors is 2 ohms.
To find the total current in the circuit, we can use Ohm's Law, which states that I (current) is equal to V (voltage) divided by R (resistance):
I = V/Req
Given that the voltage of the battery is 9 volts and the equivalent resistance is 2 ohms, we can substitute these values into the equation:
I = 9/2
I = 4.5 amps
Therefore, the equivalent resistance is 2 ohms, and the total current in the circuit is 4.5 amps.
Req = R1*R2/(R1+R2) = 3*6/(3+6) = 2 Ohms.
I = E/R = 9/2 = 4.5 Amps.
I agree, I read the 6 as 9, ...
conductance=1/3+1/9=4/9
resistance=9/4
current= 9/(9/4)=4amps