Answer to Question #93242 in Electric Circuits for esther

Question

The circuit below shows two resistors, whose resistance are 0.40ohms & 0.60ohms connected in parallel they are apart of a circuit which carries a current I and the current 0.40ohms resistor is 1.50A

............/~~~0.40ohm~~\.............
....i....../°1.50A...................\......i.....
_>___./.................................\.__>__
.....A °\............................... °/ B.......
...........\~~~0.60ohm~~~/............

....draw but don't include the dots...

Calculate
(I) the potential difference between point mark A and B in the diagram ..
(ii) The current i in the 0.60ohm resistor
(iii) the current i in the circuit.

Answer 1

Resistors connected in parallel can be replaced by one resistor with resistance (call it total)

$$R=\frac{R_1R_2}{R_1+R_2}=0.24\space\Omega.$$

The voltage across each parallel resistor is equal and is the same as the potential difference between A and B. Thus:

$$V_1=I_1R_1=1.5\cdot0.4=0.6\text{ V}.$$

$$V_2=V_1=I_2R_2,\\ I_2=V_2/R_2=0.6/0.6=1\text{ A}.$$

The total current can be calculated as a sum of both currents (by Kirchoff's current law) or according to Ohm's law by dividing the voltage by the total resistance. Both ways give 2.5 A.