Tuesday, February 3, 2015
DC Circuits: Calculating the Total Resistance of Parallel Resistances Problem #1
A 20 Ohms resistor, 5 Ohms resistor, and 1.5 Volts source are all connected in parallel with each other. Calculate the Total Resistance of the circuit, Voltage across both resistors, Total Current, and the current through each resistor.Let's draw the circuit:
Solution:
I = \frac{V}{R}
Calculating the total resistance,
R_T = \frac{R_1R_2}{R_1+R_2}
R_T = \frac{(20\Omega)(5\Omega)}{20\Omega+5\Omega}
R_T = 4\Omega
Calculating the Total Current IT,
I_T = \frac{V_{source}}{R_T}
I_T = \frac{1.5V}{4\Omega}
I_T = 0.375A
Calculating voltage across each resistor - Parallel elements have the same voltage values.
Calculating Currents I1 and I2 - Parallel elements have different current values.
I_1 = \frac{V_{source}}{R_1}
I_1 = \frac{1.5V}{20\Omega}
I_1 = 0.075A
I_2 = \frac{V_{source}}{R_2}
I_2 = \frac{1.5V}{5\Omega}
I_2 = 0.3A
To check,
I_T = I_1+I_2
I_T = (0.075A)(0.3A)
I_T = 0.375A
(same as above)If you have any question, place a comment below.
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