Question

Consider a circuit with two resistors in parallel R_1 = 10 ohm and R_2 = 5 ohm.A) Determine the total resistance of the circuit.B) Calculate the total current flowing through the battery.C) What are the current and voltage through each resistor?D) Repeat the calculations for a series configuration.

Answer 1

Answer:

Explanation:

Given

$R_1=10 \Omega$

$R_2=5 \Omega$

when resistance in Parallel

$\frac{1}{R_{p}}=\frac{1}{R_1}+\frac{1}{R_2}$

$R_p=\frac{R_1R_2}{R_1+R_2}$

$R_p=\frac{10}{3}$

Suppose V is voltage of battery

Total Current $i=\frac{3V}{10}$

Since Circuit is Parallel therefore Voltage across both resistor is same

$V=i_1R_1=i_2R_2$

and $i_1+i_2=i$

$i_1+i_1\cdot \frac{R_1}{R_2}=i$

$i_1(1+\frac{10}{5})=\frac{3V}{10}$

$i_1=\frac{V}{10}$

$i_2=\frac{2V}{10}$

(b) When Circuit is in series

$R_s=R_1+R_2$

$R_s=10+5=15 \Omega$

since circuit is in Series therefore current is same in both resistor

Current $i=\frac{V}{15} A$

Voltage drop across $R_1=i\times R_1$

$V_1=\frac{V}{15}\times 10=\frac{2V}{3}$

$V_2=\frac{V}{15}\times 5=\frac{V}{3}$