Answer to Question #117262 in Electric Circuits for Cecilia LeBrun

Question

I have a parallel circuit attached to a simple circuit. I have the value of the resistors in the parallel circuit of 3 ohms and 6 ohms with the amp of .5 listed next to the 6 ohms. Resistor 3 is outside of the parallel circuit in a simple circuit which has no value. The volt is 12. The current next to the 3 ohms (I2) has no value. Find the value of I2, the resistor 3 and total current I

Answer 1

Given:

$R_1=6\Omega,\\ R_2=3\Omega,\\ I_1=0.5\text{A}.\\ \text{---------------}\\ I_2-?\\ I-?\\ R_3-?$

Solution:

The voltage across 6Ω resistor:

$$V_1=R_1I_1=6\cdot0.5=3\text{V}.$$

Since 6Ω and 3Ω resistors are in series, they have equal voltages, and the voltage across 3Ω resistor is:

$$V_2=R_2I_2,\\ V_1=V_2,\\ V_1=R_2I_2,\\ I_2=\frac{V_1}{R_2}=\frac{3}{3}=1\text{A}.$$

The total current is the sum of currents in 3Ω and 6Ω:

$$I=I_1+I_2=0.5+1=1.5\text{A}.$$

The voltage source provides voltage for the parallel part and the resistor $R_3:$

$$V=V_1+V_3=V_2+V_3,\\ V=V_1+IR_3,\\ R_3=\frac{V-V_1}{I}=\frac{12-3}{1.5}=6\Omega.$$

The voltage across the third reistor:

$$V_3=R_3I=6\cdot1.5=9\text{V}.$$