A 6 ohm, 5 ohm, and 8 ohm resistor are connected in parallel with a 30 V battery. What is the total resistance and the current through the 8 ohm resistor?
A) Total Resistance = 19 ohms. Current = 1.58 A
B) Total Resistance = 2.03 ohms. Current = 14.78 A
C) Total Resistance = 2.03 ohms. Current = 3.75 A
D) Total Resistance = 19 ohms. Current = 3.75 A
1/R = 1/6 + 1/5 + 1/8 = 59/120
the current is 30/R = 30 * 59/120 = 59/4 amps
t/6 + t/5 + t/8 = 1
20t + 24t + 15t = 120
current = 30 V / 8 Ω = ? A
To find the total resistance in a parallel circuit, you use the formula:
1/R(total) = 1/R1 + 1/R2 + 1/R3 + ...
In this case, the resistors are 6 ohm, 5 ohm, and 8 ohm. So, the equation becomes:
1/R(total) = 1/6 + 1/5 + 1/8
To calculate the total resistance, you need to find the reciprocal of the sum of the reciprocals of each resistor:
1/R(total) = (40 + 48 + 30) / (6 * 5 * 8)
1/R(total) = 118 / 240
Now, take the reciprocal of both sides of the equation to find the total resistance:
R(total) = 240 / 118
R(total) ≈ 2.034 ohms
Therefore, the total resistance is approximately 2.034 ohms.
To find the current through the 8 ohm resistor, you can use Ohm's Law:
I = V / R
Where I is the current, V is the voltage, and R is the resistance.
In this case, the voltage is 30 V and the resistance is 8 ohms.
I = 30 / 8
I ≈ 3.75 Amps
Therefore, the current through the 8 ohm resistor is approximately 3.75 Amps.