Question

5.) calculate the value of r_t i_t. use units and proper engineering notation for full credit. this is a compound circuit so make sure to simplify first! r1 150ω vt 12v it rt r5 270ω r4 1.8kω r2 200ω r3 470ω

Explanation:

Step1: Calculate equivalent resistance of R2 and R3 in series

$R_{23}=R2 + R3=200\Omega+470\Omega = 670\Omega$

Step2: Calculate equivalent resistance of R4 and R23 in parallel

$R_{4 - 23}=\frac{R4\times R_{23}}{R4 + R_{23}}=\frac{1800\Omega\times670\Omega}{1800\Omega + 670\Omega}=\frac{1206000}{2470}\Omega\approx488.26\Omega$

Step3: Calculate equivalent resistance of R5 and R4 - 23 in series

$R_{5 - 4 - 23}=R5+R_{4 - 23}=270\Omega + 488.26\Omega=758.26\Omega$

Step4: Calculate total resistance RT

$R_T=R1+R_{5 - 4 - 23}=150\Omega+758.26\Omega = 908.26\Omega$

Step5: Calculate total current IT using Ohm's law

$I_T=\frac{V_T}{R_T}=\frac{12V}{908.26\Omega}\approx13.21\times10^{-3}A = 13.21mA$

Answer:

$R_T = 908.26\Omega$, $I_T=13.21mA$