Ohm\'s Law Hopefully this picture is blurry. a) Two resistors of 20ohm and 40ohm

Question

Ohm's Law

Hopefully this picture is blurry.

a) Two resistors of 20ohm and 40ohm are connected in parallel. What resistance must be connected in parallel with them to make the total resistance equal to 12ohm?
b) A lamp is connected to a 90-V line. The current in the filament starts at 10 A. drops quickly to 2 A. Why does this happen? By what factor does the resistance increase?
c) A 4.0ohm resistor, and 8.0ohm resistor, and a 12ohm resistor are connected in a series with a 24-V battery. What is the current in each resistor? Repeat for the case in which all three resistors are connected in parallel across the battery.

Explanation / Answer

2)

Given

equivalent resistance

Req=12 ohms

R1=20 ohms

R2=40 ohms

R3=?

equivalent resistance in parallel is given by

1/Req =1/R1 + 1/R2 +1/R3

1/12 =1/20 +1/40 +1/R3

R3=120 ohms

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3

Initially resistance

R1=V/I =90/10 =9 ohms

as the filament glows ,the current drops to 2 A,since resistance increases .The Resistance is

R2 =90/2 =45 ohms

so resistance increases by a factor

R2/R1 =45/9 =5

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4.

a)

In series

equivalent resistance

R=4+8+12 =24 ohms

Total current flowing in the circuit is

I=V/R =24/24 =1 A

So Current through each resistor is

I4=I8=I12=1 A

b)

Current through each resistor is

I4=V/R =24/4 =6 A

I8=24/8 =3 A

I12=24/12 =2 A

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