A student connects a circuit with a cell, an ammeter, and a
buzzer and listens to the buzzer.
She adds another cell.
Describe and explain what
happens to the current

let the voltages of the cell be V and R the equivalent resistance of the circuit.

I1=RV∵ only one cell connected  ;

I2=RV+V=R2V∵ two cells connected in series  ;

I3=RV+RV=R2V∵ two cells connected in parallel ⇒ total current is same as sum of the currents due to each.

Now , 

LHS = 3I3I2=3R2VR2V=3(R24V2) 

RHS = 2I3(I1+I2)=2R2V(RV+R2V)=2R2VR3V=3R2therefore, LHS = RHS   

measure their densities same density, same sub