Electric circuits problems, finding current.

[physics604]

1. A series circuit initially consists of a cell of unknown voltage, a resistor R₂ of 4.0 Ω, and another resistor R₂ of 6.0 Ω. A student measures the current through R₂ to be 3.0 A. When a wrench that has a small resistance is dropped on the circuit, the current through R₂ is reduced to 1.0 A. What is the current flowing through the wrench? (Assume the supply voltage remains constant.)

a) 1.0 A
b) 2.0 A
c) 5.0 A
d) 7.5 A

To summarize:

R₁=4.0 Ω
R₂= 6.0Ω
I₂ initially= 3.0 A
I₂ with wrench= 1.0 A
Find I (current) going through the wrench.

Homework Equations

V=IR

The Attempt at a Solution

My answer is a) 1.0 A, but it is wrong. The correct answer is c) 5.0 A but I don't understand why.

I was told that in a series circuit, the current should be the same throughout. So in the circuit (with wrench), if the current is measured after a resistor to have a current of 1.0 A, shouldn't the current through the wrench be the same?

 

[gneill]

1. A series circuit initially consists of a cell of unknown voltage, a resistor R₂ of 4.0 Ω, and another resistor R₂ of 6.0 Ω. A student measures the current through R₂ to be 3.0 A. When a wrench that has a small resistance is dropped on the circuit, the current through R₂ is reduced to 1.0 A. What is the current flowing through the wrench? (Assume the supply voltage remains constant.)

a) 1.0 A
b) 2.0 A
c) 5.0 A
d) 7.5 A

To summarize:

R₁=4.0 Ω
R₂= 6.0Ω
I₂ initially= 3.0 A
I₂ with wrench= 1.0 A
Find I (current) going through the wrench.

Homework Equations

V=IR

The Attempt at a Solution

My answer is a) 1.0 A, but it is wrong. The correct answer is c) 5.0 A but I don't understand why.

I was told that in a series circuit, the current should be the same throughout. So in the circuit (with wrench), if the current is measured after a resistor to have a current of 1.0 A, shouldn't the current through the wrench be the same?

Dropping the wrench onto the circuit is unlikely to insert the wrench into the series scenario. Instead, it will likely lie across some component, providing a parallel path...

 

[physics604]

Initially:

R₁ = 4.0 Ω
I₁ = 3.0 A
V₁ = 12.0 V

R₂ = 6.0 Ω
I₂ = 3.0 A
V₂ = 18.0 V

So V_T = 30.0 V

With wrench:

V_T = 30.0 V

R₁ = 4.0 Ω
I₁ = 1.0 A
V₁ = 4.0 V

R₂ = 6.0 Ω
I₂ = 1.0 A
V₂ = 6.0 V

V_wrench = 20 V

But I still don't know R of the wrench so I can't figure out I.

 

[barryj]

Gneill correctly states, Dropping the wrench onto the circuit is unlikely to insert the wrench into the series scenario. Instead, it will likely lie across some component, providing a parallel path...

Draw a diagram of the initial circuit. Then figure out where you could drop a wrench that would reduce the current through R2. Then work the circuit.

 

[physics604]

Okay, I got it! (plus the three other questions I posted as well).

Thanks!