A circuit is constructed with five resistors and a battery as shown. The values

Question

A circuit is constructed with five resistors and a battery as shown. The values for the resistors are: R1 = R5 = 66 ?, R2 = 83 ?, R3 = 68 ?, and R4 = 138 ?. The battery voltage is V = 12 V.

1)What is Rab, the equivalent resistance between points a and b?

?

2)What is Rac, the equivalent resistance between points a and c?

?

3)What is I5, the current that flows through resistor R5?

A

4)What is I2, the current that flows through resistor R2?

A

5)What is I1, the current that flows through the resistor R1?

A

6) What is V4, the voltage across resistor R4?

V

show full steps to final answer to get awarded. giving the rule or the final answer with out doing the calculations and showing it will be reported and spamed !!

Explanation / Answer

a)

R2 and R3 are in series

R23=83+68=151 ohms

R23 and R4 are in parallel ,so

1/Rab =1/151 + 1/138

Rab=72.1 ohms

b)

R1 and Rab are in series ,so

Rac=72.1+66 =138.1 ohms

c)

equivalent resistance

Rac and R5 are in series.

Req=138.1+66 =204.1 ohms

Total Current

I5=V/Req=12/204.1 =0.0588 A

d)

By current divider rule ,Current through I2 is

I2=I5*(R4/R23+R4)=0.0588*(138/138+151)

I2=0.0281 A

e)

Current through R1 is

I1=I5=0.0588 A

f)

Current through R4 is

I4=I1-I2=0.0588-0.0281

I4=0.0307 A

Voltage across R4 is

V4=I4*R4=0.0307*138

V4=4.24 Volts

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