Question

The parallel circuit at the right depicts two resistors connected to a voltage source. The voltage source (ΔVtot) is a 12-V source and the resistor values are 7.4 Ω (R1) and 3.9 Ω (R2).a. Determine the equivalent resistance of the circuit. b. Determine the current in each branch resistor:Current in R1 = Current in R2 = c. Determine the total current in the circuit.

Answer 1

Given:

Two resistors are connected in parallel.

The resistance of resistor 1 is

$R1=\text{ 7.4}\Omega$

The resistance of resistor 2 is

$R2\text{ = 3.9 }\Omega$

The value of the voltage source is

$\Delta V_{tot}=\text{ 12 V}$

Required:

(a)The equivalent resistance of the circuit.

(b) The current in each branch of the resistor.

(c) The total current in the circuit.

Explanation:

(a) In a parallel circuit, the equivalent resistance can be calculated as

$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R1}+\frac{1}{R2} \\ =\frac{1}{7.4}+\frac{1}{3.9} \\ R_{eq}=\text{ 2.55 }\Omega \end{gathered}$

(b) In a parallel circuit, the voltage across each resistor is the same.

The current through the resistor R1 can be calculated according to Ohm's law

$\begin{gathered} I_{R1}=\frac{V}{R1} \\ =\frac{12}{7.4} \\ =1.62\text{ A} \end{gathered}$

The current through the resistor R2 can be calculated as

$\begin{gathered} I_{R2}=\frac{V}{R2} \\ =\frac{12}{3.9} \\ =3.08\text{ A} \end{gathered}$

(c) The total current in the circuit is the sum of the current through each branch.

Thus, the total current can be calculated as

$\begin{gathered} I=I_{R1}+I_{R2} \\ =\frac{12}{7.4}+\frac{12}{3.9} \\ =\text{ 4.7 A} \end{gathered}$

Final Answer:

(