Answer to Question #198107 in Electric Circuits for Martin Cordero

Question

A 24.0 V battery is connected to a circuit that has an ammeter (A1), a 6.0 ohm

resistor connected in series with a voltmeter (V1) and 3 resistors connected in parallel

R1, 2.0 ohms, R2, 2.0 ohms and R3, 1.0 ohms. There is a voltmeter (V2) placed across

the R1 and an ammeter (A2) in line with R2. A. Calculate the values of the meters. (V1,

V2, A1 & A2).

Answer 1

Resistance of parallel circuit:

$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

$R_p=\frac{R_1R_2R_3}{R_2R_3+R_1R_3+R_1R_2}=\frac{2\cdot2}{2+2+4}=0.5\ \Omega$

Then:

Value of A1:

$I=\frac{24}{6+0.5}=3.7\ A$

Value of V1:

$U=3.7\cdot6=22.2\ V$

Voltage in parallel circuit:

$U_p=24-22.2=1.8\ V$

Then:

Value of V2:

$U_p=1.8\ V$

Value of A2:

$I_2=U_p/R_2=1.8/2=0.9\ \Omega$