Question

1. which circuit in figure 3–23 has the most current? the least current?

figure 3–23
(a) 30 v, 33 kω; (b) 75 v, 3.9 kω; (c) 100 v, 47 kω

Explanation:

To determine which circuit has the most and least current, we use Ohm's Law, \( I = \frac{V}{R} \), where \( I \) is current, \( V \) is voltage, and \( R \) is resistance.

Step 1: Calculate current for circuit (a)

Given \( V = 50 \, \text{V} \) and \( R = 33 \, \text{k}\Omega = 33000 \, \Omega \).
\[
I_a = \frac{50}{33000} \approx 0.001515 \, \text{A} = 1.515 \, \text{mA}
\]

Step 2: Calculate current for circuit (b)

Given \( V = 75 \, \text{V} \) and \( R = 3.9 \, \text{k}\Omega = 3900 \, \Omega \).
\[
I_b = \frac{75}{3900} \approx 0.01923 \, \text{A} = 19.23 \, \text{mA}
\]

Step 3: Calculate current for circuit (c)

Given \( V = 100 \, \text{V} \) and \( R = 47 \, \text{k}\Omega = 47000 \, \Omega \).
\[
I_c = \frac{100}{47000} \approx 0.002128 \, \text{A} = 2.128 \, \text{mA}
\]

Answer:

Most current: Circuit (b) (≈19.23 mA)
Least current: Circuit (a) (≈1.515 mA)