for the circuit below the wires which cross and form the X in the center of the

Question

for the circuit below the wires which cross and form the X in the center of the circuit are NOT connected to each other. Remember that one can manipulate the wires in an identical circuit, so the elements can be re-arranged such that the relationship between the resistors (series or Paralell) will be clearly illumnated.

A) Reduce the circuit to its series equivalent (i.e only on resistor connected to the battery) and determine the equivalent resistance.

b) What is the potential difference across the 1.0 OHM resistor and the current flows through it?

Explanation / Answer

a)From the figure the resistors      3 and 6 are connected in seriescombination           R1 = 3+ 6 = 9      and   2 and 1 are also in series combination         R2 = 1 + 2 = 3      R1 and R2 qre connected in parallel combination            equivalent resistance is           R = R1 R2 / R1 + R2                 = 9 * 3 / 9+ 3               = 2.25 if the resistors are in parallel combination voltage across each resistance is same           Voltage across R2 is   2 V current through resistance 1 is               I =   2 V / 1                  = 2 A b) potential across 1 Since R1 R2 are in parallel Voltage across R1 is 2V Voltage acros 1 is 1/1+2(2)=0.66V =0.5V c) Power generated P=I2R=22*2.25=9 W

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