Tuesday, February 3, 2015

DC Circuits: Calculating the Total Resistance of Parallel Resistances Problem #1

Shinemax24 1:05 AM DC Circuit , Parallel Resistance No comments :

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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