Question

question 25 of 25
in the circuit below, resistors r₁ and r₂ are in parallel. what is the equivalent resistance? (r₁ = 75 ω,r₂ = 50 ω)(1/r_tot = 1/r₁ + 1/r₂ + 1/rₙ)

a. 125 ω
b. 0.008 ω
c. 25 ω
d. 30 ω

Explanation:

Step1: Apply parallel - resistance formula

Given the formula for parallel resistors $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$, where $R_1 = 75\Omega$ and $R_2=50\Omega$. Substitute the values: $\frac{1}{R_{eq}}=\frac{1}{75}+\frac{1}{50}$.

Step2: Find a common denominator

The common denominator of 75 and 50 is 150. So, $\frac{1}{R_{eq}}=\frac{1\times2}{75\times2}+\frac{1\times3}{50\times3}=\frac{2}{150}+\frac{3}{150}=\frac{2 + 3}{150}=\frac{5}{150}$.

Step3: Solve for $R_{eq}$

Since $\frac{1}{R_{eq}}=\frac{5}{150}$, then $R_{eq}=\frac{150}{5}=30\Omega$.

Answer:

D. 30 Ω