Four resistors and a 6-V battery are arranged as shown in the circuit diagram. D

Question

Four resistors and a 6-V battery are arranged as shown in the circuit diagram. Determine the equivalent resistance for this circuit. A) 50 ohm B) 120 ohm C) 29 ohm D) 5 ohm E) 12 ohm The smallest current passes through which resistor(s)? A) the 10-ohm resistor B) the 20-ohm resistor C) the 30-ohm resistor D) the 60-ohm resistor E) It is the same and the smallest in the 30-ohm and 60-ohm resistors. The largest potential difference is across which resistor(s)? A) the 10-ohm resistor B) the 20-ohm resistor C) the 30-ohm resistor D) the 60-ohm resistor E) It is the same and the largest for the 30-ohm and 60-ohm resistors,

Explanation / Answer

I will use the following notation {} for series connection , [] for parallel connection

Equivalent resistance= [20,{10+[30,60]}]=12 ohm

( 30,60 ohm resistors are in parallel, this combination is then in series connection with 10 ohm, while the gross combination is in then in parallel connection with 20 ohm.

Total current in the circuit=6/12=0.5 A

P.D across 20 ohm=6 V   current through it=6/20 = 0.3 A

current through 10 ohm resistance: 0.5-0.3 = 0.2 A ( this is the remaining current that goes to this half,and since 10 and [30,60] are together in series current through 10 and [30,60] combined will be same)

Thus PD across 10 ohm= 2 V

Thus now we have PD across 30 and 60 ohm as 6-2=4 V ( since they are in parallel )

Thus, current through 30 ohm=4/30=0.13 A

current through 60 ohm=4/60=0.07 A

Thus, smallest current is passing through 60 ohm resistor

Largest Potential difference is observed across 20 ohm resistor

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