Question

solve the following circuit for $r_t$, $i_t$, $i_1$, $i_2$, and $v_3$.
please show all your steps. no step no point!

circuit diagram: vs (15v) connected in a circuit with r1 (10kω), r2 (5kω), and r3 (15kω) in a configuration (likely series-parallel or series, based on the diagram).

Explanation:

Step1: Find Total Resistance ($R_T$)

In a series circuit, total resistance is the sum of individual resistances. So \( R_T = R_1 + R_2 + R_3 \). Substituting values: \( R_1 = 10\mathrm{k}\Omega \), \( R_2 = 5\mathrm{k}\Omega \), \( R_3 = 15\mathrm{k}\Omega \). Thus, \( R_T = 10 + 5 + 15 = 30\mathrm{k}\Omega \).

Step2: Find Total Current ($I_T$)

Using Ohm's Law \( I = \frac{V}{R} \), where \( V = V_s = 15\mathrm{V} \) and \( R = R_T = 30\mathrm{k}\Omega = 30000\Omega \). So \( I_T = \frac{15}{30000} = 0.5\mathrm{mA} \).

Step3: Find $I_1$ and $I_2$ (Series Current)

In a series circuit, current is the same through all components. So \( I_1 = I_2 = I_T = 0.5\mathrm{mA} \).

Step4: Find $V_3$ (Voltage across $R_3$)

Using Ohm's Law \( V = IR \), for \( R_3 = 15\mathrm{k}\Omega = 15000\Omega \) and \( I = I_T = 0.5\mathrm{mA} = 0.0005\mathrm{A} \). So \( V_3 = 0.0005 \times 15000 = 7.5\mathrm{V} \).

Answer:

• \( R_T = 30\mathrm{k}\Omega \)
• \( I_T = 0.5\mathrm{mA} \)
• \( I_1 = 0.5\mathrm{mA} \)
• \( I_2 = 0.5\mathrm{mA} \)
• \( V_3 = 7.5\mathrm{V} \)