Question

Two resistors 12 ohm and 6 Ω are connected in parallel and this combination is
connected in series with a 6.5 Ω resistance. Suppose the circuit is connected to a
battery. Determine the voltage of the battery if the potential difference across 6 Ω
resistance is 6 V.

Answer 1

Explanation:

as the resistors 12ohm and 6 ohm are in parallel,

resultant resistance=12×6/12+6=4ohm

given, voltage through 6ohm resistor is 6v

this implies voltage through the entire parallel combination is 6v.

as this parallel combination is inturn connected to 6.5ohm in series,

if V is the voltage of the battery,

V=v1+v2

where v1is the potential difference across the parallel combination

v2 is the potential difference across the resistor of resistance 6.5 ohm.

finding v2:

as current through the parallel combination and the resistance is same, v1/4=v2/6.5

v2/6.5=6/4

v2=9.075v

hence, V=6+9.075

=15.075V