Four resistors are connected to a battery as shown in the figure below. http://w

Question

Four resistors are connected to a battery as shown in the figure below.

http://www.webassign.net/serpse8/28-p-016.gif

(a) Determine the potential difference across each resistor in terms of emf. (Use the following as necessary: script e for emf.)

?V1 = ?
?V2 = ?
?V3 = ?
?V4 = ?

(b) Determine the current in each resistor in terms of I.

I1 = ?
I2 = ?
I3 = ?
I4 = ?


(c) If R3 is increased, explain what happens to the current in each of the resistors.

(d) In the limit that R3 ? infinity, what are the new values of the current in each resistor in terms of I, the original current in the battery?

I1 = ?
I2 = ?
I3 = ?
I4 = ?

Explanation / Answer

R(eq) = R + 3R||6R = 3R (b) I1 = e/3r Voltage across the parallel connection = e - e/3 = 2e/3 I4 = (2e/3)/3R = 2e/9R I2 = I3 = (2e/3)/6R = e/9R (a) DV1 = I1*R = e/3 Dv4 = 2e/3 Dv2 = e/9R * 2R = 2e/9 DV3 = e/9R * 4R = 4e/9 (c) If R3 is increased the the values of all the currents will decrease (d) if R3 -> infinity, then the branch is open. ie. I2 = I3 = 0 R(eq) = R1 + R4 = 4R I1' = I4' = e/4R = 3/4 I

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