Consider 6 resisters are connected in a circuit as shown in the Figure below (R

Question

Consider 6 resisters are connected in a circuit as shown in the Figure below (R1 = 5?, R2 = 10?, R3 = 3?, R4 = 13?, R5 = 26? and R6 = 6?). The potential difference across the R1 = 5? resistor is V= 12V.

Determine:

a) The current through the battery.
b) The emf of the battery.
c) The current in the R2 resistor.
d) The voltage between points a and b?
e) The power dissipated in the R4 resistor.

Consider 6 resisters are connected in a circuit as shown in the Figure below (R1 = 5?, R2 = 10?, R3 = 3?, R4 = 13?, R5 = 26? and R6 = 6?). The potential difference across the R1 = 5? resistor is V= 12V. Determine: a) The current through the battery. b) The emf of the battery. c) The current in the R2 resistor. d) The voltage between points a and b? e) The power dissipated in the R4 resistor.

Explanation / Answer

a)

Current through the battery

I=V/R1=12/5 =2.4 A

b)

equivalent resistance

R5 and R4 are in parallel

1/R45 =1/13 + 1/26

R45=8.67 ohms

R45 and R6 are in series

R456=6+8.67 =14,67 ohms

R2 and R3 are in series

R23=10+3=13 ohms

R23 and R456 are in parallel

1/R23456 =1/13 +1/14.67

R23456=6.89 ohms

R1 and R23456 are in series ,so

Req=5+6.89 =11.89 ohms

Emf of the battery

E=I*Req=2.4*11.89

E=28.54 Volts

c)

Current through R2 is

I2=I*(R456/R23+R456) =2.4*(14.67/14.67+13)

I2=1.27 A

d)

Voltage across a and b terminal is

Vab=E-V =28.54-12 =16.54 Volts

e)

Current through R456

I456=2.4-1.27=1.13 A

Current through R4

I4=I456*(R5/R4+R5)=1.13*(26/26+13)

I4=0.75 A

Power dissipated in R4 is

P4=I42R4=0.752*13

P4=7.38 Watts

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