Three resistors (14.4 Ω, 21.7 Ω, 14.1 Ω) are connected in parallel across 98 V. What is the total resistance for this circuit? What is the voltage drop across the 21.7 Ω resistor? What current is flowing in the 14.1 Ω resistor? What is the total circuit current? What power is dissipated at the 14.4 Ω resistor?
E = 98 V.
R1 = 14.4 Ohms
R2 = 21.7 Ohms
R3 = 14.1 Ohms.
a. 1/Rt = 1/R1+1/R2+1/R3
1/Rt = 1/14.4 + 1/21.7 + 1/14.1 =
0.186449 Mhos
Rt = 5.36 Ohms
b. V1 = V2 = V3 = E = 98 V.
c. I3 = E/R3 = 98/14.1 = 6.95A
d. I = E/Rt = 98/5.36 = 18.3A
e. P1 = E^2/R1 = 98^2/14.4 = 667 Watts
1/R=1/R1+1/R2=1/R3
1/R=1/R1+1/R2+1/R3
To find the total resistance of resistors connected in parallel, you can use the formula:
1/RTotal = 1/R1 + 1/R2 + 1/R3 + ...
For this circuit, you have three resistors connected in parallel, so the total resistance (RTotal) can be calculated as follows:
1/RTotal = 1/14.4 + 1/21.7 + 1/14.1
Now, to find the voltage drop across the 21.7 Ω resistor, you can use Ohm's Law which states that the voltage (V) across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R):
V = I * R
To find the current flowing through the 14.1 Ω resistor, you can use Ohm's Law again, since you have the resistance and the voltage across it:
I = V / R
For the total circuit current, you can use the fact that the total current flowing into a parallel circuit is equal to the sum of the currents flowing through each individual branch.
Now, to find the power dissipated at the 14.4 Ω resistor, you can use the formula:
P = I^2 * R
Once you've calculated the total resistance, you can use the voltage (98 V) and the formula mentioned above to find the voltage drop across each resistor. Then, you can use the current calculation formula to find the current flowing through the 14.1 Ω resistor. Finally, you can calculate the total circuit current and use it to find the power dissipated at the 14.4 Ω resistor.
Plugging in the values and following these steps will give you the answers to each of the questions.