Answer:
1. 7.32ohms
2. 1.64amperes
3. 3ohms= 4.92volts, 2ohms& 7ohms= 2.55volts, 4ohms & 9ohms= 4.54volts
4. 41.875ohms
5. 0.2388amperes
6. 20ohms=4.776volts, 30ohms & 50ohms= 0.4478volts, 20ohms=4.776volts
7. 10ohms
8. 0.5amperea
9. R1=2volts R2=1volt R3=2volts R4=2.5volts R5=0.5volts R6=0.25volts R7=0.25volts
10. 198.7ohms
11. 0.12amperes
12. 2.88watts
Explanation:
1. Solving the parallel connections,
1/2+1/7= (7+2)/14
9/14
Resistance= 14/9
1/4+1/9= (9+4)/36
13/36
Resistance=36/13
Total resistance in the circuit= 3+14/9+ 36/13
(351+182+ 324)/117
857/117= 7.32ohms
2. V=IR
I= V/R(total resistance)
I= 12/7.32
I= 1.64amperes
3. V= IR
for the 3ohms resistors, V= 3×1.64
=4.92volts
Voltage is the same for resistors in parallel
Current is the same for resistors in series
for the parallel resistors 2ohms and 7ohms,
V= 1.64 × 14/9
= 2.55volts
for the parallel resistors 4ohms and 9ohms,
V= 1.64× 36/13
= 4.54volts
4. For parallel resistors R2 and R3,
1/30+1/50 = (50+30)/150
80/150
Resistance= 150/80
Total resistance= 20+150/80+20
(1600+150+1600)/80
3350/80= 41.875ohms
5. V= IR
I= 10/41.875
= 0.2388amperes
6. for the 20ohms resistor,
V= 0.2388×20
V=4.776volts
for the parallell resistors 30ohms and 50ohms,
V= 0.2388×150/80
= 0.4478volts
for the 20ohma resistor,
V= 0.2388×20
= 4.776volts
7. R6+R7 = 2+2
= 4ohms
1/4 + 1/R5
1/4+1/4=(1+1)/4
2/4= 4/2
=2ohms
2+R4= 2+10
=12ohms
R2 +R3= 4+8
=12
1/12+1/12= 2/12
12/2=6
6+R1= 6+4
total resistance= 10ohms
8. V=IR
I= 5/10
=0.5amperes
9. For R1
V= 0.5×4
=2volts
for 6ohms effective resistance
V=0.5×6
=3volts
For R2 and R3
V=IR
3=I×12
I=0.25
In R2
V=0.25×4
=1Volt
In R3
V=0.25×8
=2volts
0.5-0.25=0.25amperes
In R4
V=0.25×10
=2.5volts
for the 2ohms effective resistance,
V=0.25×2
=0.5volts
In R5
v= 0.5volts
I= 0.5/4
= 0.125amperes
current in R6 and R7
0.25-0.125=0.125amperes
In R6
V=0.125×2
=0.25volts
in R7
V=0.125×2
=0.25volts
10. for R1 and R2
1/100+1/250
(5+2)/500= 7/500
500/7= 71.43ohms
for R3 and R4
1/350+ 1/200
(4+7)/1400=11/1400
1400/11=127.27ohms
total resistance= 71.43+127.27
= 198.7ohms
11. V=IR
I= 24/198.7
=0.12amperes
12. Power= IV
power= 0.12×24
=2.88watts
