Answer to Question #204605 in Electric Circuits for pumpkin

Question

1. Three Identical lamps are connected in series to a 12 volt battery. What is the voltage drop across each lamp.?
2. Three 50- Ω resistors are connected in series . The equivalent resistance of the combination is?
3. Two resistors, R1 = 2.0 kΩ and R2= 3.0kΩ are connected in parallel and their combination is connected in series to a fully charged, 150 µF capacitor. When the switch is opened the capacitor begins to discharge. What is the time constant for the discharge?
4. Four 50 Ω resistor are connected in parallel. The equivalent resistance of the combination is?
5. How many 4Ω capacitor must be connected in parallel to have a total resistance of 0.8 Ω ?

Answer 1

1. The voltage drop across each lamp is

$$V_L=\frac V3=4\text V.$$

2. The equivalent resistance of the combination is

$$R_e=R_1+R_2+R_3=50+50+50=150\Omega.$$

3. The equivalent resistance:

$$\frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2},\\\space\\ R_e=\frac{R_1R_2}{R_1+R_2}.$$

Time constant:

$$\tau=RC=\frac{R_1R_2}{R_1+R_2}C=4500000\text s.$$

4. The equivalent is

$$\frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4},\\\space\\ \frac{1}{R_e}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R},\\\space\\ R_e=\frac R4=12.5\Omega.$$

5. From the last equation above it follows that

$$n=\frac{R}{R_e}=\frac{4}{0.8}=5.$$