A 9V battery is connected to a circuit wired in parallel. The resistors are 4 ohms, 8 ohms, and 6 ohms. What is the equivalent resistance? What is the total current?

Question

A 9V battery is connected to a circuit wired in parallel. The resistors are 4 ohms, 8 ohms, and 6 ohms. What is the equivalent resistance? What is the total current?

Answer 1

assuming you mean that the three resistors are in parallel, then

1/R = 1/4 + 1/8 + 1/6
R = 24/13 Ω
current = E/R = 9 * 13/24 = 4.875 amps

Answer 2

To find the equivalent resistance of resistors in parallel, you can use the formula:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

Where:
Req is the equivalent resistance
R1, R2, R3, ... are the values of individual resistors

In this case, we have three resistors with resistance values of 4 ohms, 8 ohms, and 6 ohms. Plugging these values into the formula, we get:

1/Req = 1/4 + 1/8 + 1/6

To add these fractions, we need to find a common denominator. In this case, the least common denominator is 24:

1/Req = (6/24) + (3/24) + (4/24)
= 13/24

To find Req, we take the reciprocal of both sides of the equation:

Req = 24/13 ≈ 1.846 ohms (rounded to three decimal places)

Now, to find the total current in the circuit, we can use Ohm's Law:

I = V/Req

Where:
I is the total current
V is the voltage (in this case, 9V)
Req is the equivalent resistance (found to be 1.846 ohms)

Plugging in the values, we get:

I = 9/1.846
≈ 4.876A (rounded to three decimal places)

Therefore, the equivalent resistance is approximately 1.846 ohms, and the total current is approximately 4.876 amperes.

Answer 3

To find the equivalent resistance of a circuit wired in parallel, you can use the formula:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

In this case, the resistors are 4 ohms, 8 ohms, and 6 ohms. So, we can plug in these values into the formula:

1/Req = 1/4 + 1/8 + 1/6

First, we need to find a common denominator for the fractions, which in this case is 24. Then, we can simplify the equation:

1/Req = 6/24 + 3/24 + 4/24

1/Req = 13/24

Now, we can find the reciprocal of both sides to get the equivalent resistance (Req):

Req = 24/13 ohms

So, the equivalent resistance of the circuit is 24/13 ohms.

To find the total current (I), we can use Ohm's Law, which states that the current (I) flowing through a resistor is equal to the voltage (V) across the resistor divided by the resistance (R):

I = V / R

In this case, the voltage (V) is 9V (because it's connected to a 9V battery) and the equivalent resistance (Req) is 24/13 ohms. So we can find the total current:

I = 9V / (24/13) ohms

To divide by a fraction, we can multiply by its reciprocal:

I = 9V * (13/24) ohms

Simplifying the equation:

I = (117/24) A

So, the total current in the circuit is 117/24 Amperes.