Question

How will voltage and current behave in a circuit with two adjacent batteries (battery-battery-bulb-bulb)? How does this change for two non-adjacent batteries (battery-bulb-battery-bulb)?

Answer 1

if there is a switch in the circuit that switches on or off , then as long as the switch is off (the circuit is open ), there is no current .

once the switch is closed, then net current=(E1+E2)/(R1+R2)

where E1=emf of battery 1

E2=emf of battery 2

R1=resistance of bulb 1

R2=resistance of bulb 2

if the batteries are connected in opposing each other,

then current =(E1-E2)/(R1+R2)

hence , only the polarity of battery connection matter but there relative position does not matter.

once the citcuit is closed, a uniform current will flow in both the cases as per the formula given above.

similarly, as the voltage across a resistance=current*resistance

as current value does not change, voltage across the bulbs will also not change.

voltage at particular nodes:

if you consider each junction as a node,(junction of battery and bulb is a node, bulb and battery is a node, battery and battery is a node), then the node voltage will depend upon the arrangement, as whie emf drop happens across ressitance, emf may increase or decrease across battery from node to node depending upon its polarity.