physics

Question

Calculate the potential difference between points A and B in a circuit with a 12V battery connected in series with a 5Ω resistor and a 10Ω resistor.

Answer

step 1: calculate the total resistance the resistors are connected in series, so the total resistance

rtotalr_{ ext{total}}

is the sum of the individual resistances:

rtotal=r1+r2=5ω+10ω=15ωr_{ ext{total}} = r_1 + r_2 = 5ω + 10ω = 15ω

step 2: calculate the total current using ohm's law we use ohm's law

v = i r

to calculate the total current in the circuit. the voltage supplied by the battery is 12v, and the total resistance is 15ω:

\frac{v}{r_{ ext{total}}} = \frac{12v}{15ω} = 0.8a

step 3: calculate the potential difference across the 10ω resistor since the resistors are in series, the current is the same through both resistors. now, we calculate the potential difference across the 10ω resistor using ohm's law:

vab=i×r10ω=0.8a×10ω=8vv_{ ext{ab}} = i imes r_{10ω} = 0.8a imes 10ω = 8v

conclusion: the potential difference between points a and b is 8v.

Answer

what is the potential difference of a series circuit?  
when two or more components are connected in series, the total potential difference of the circuit is shared between them. this means that if you sum the voltages across each resistor connected in series, the total equals the voltage of the circuit.use the ohms law formulas to find the potential difference of the series circuit?lets start with finding the total resistance (rt) = r1 + r2 = r1 = 5 ohms + r2 = 10 ohms = 15 ohmsnow we are ready to solve for the total current
     total current (i) = voltage total divided by resistance total = 12 volts divided by 15 ohms = 0.8 amps or amperes
next we can find the individual voltage drops across each resistor in the circuit 
(hint: current  0.8 amps is the same throughout the series circuit)  
voltage drop v1 = current total x r1 = 0.8 amps x 5 ohms = 4 volts (v1)
voltage drop v2 = current total x r2 = 0.8 amps x 10 ohms = 8 volts (v2)
the potential difference of the series circuit v1 and v2 added together total the overall voltage total. 
solutions:
 the specified result shows that the voltage drop across 5 ohms = 4 volts  and  voltage drop across 10 ohms = 8 volts.  
the question failed to specify the component however solved for both unless stated other wise.
 (checking answer) voltage total = v1 + v2 = 4 v1 + 8 v2  = 12 volts

Answer

in a circuit powered by a 12-volt battery with two resistors&mdash;5 ohms and 10 ohms&mdash;connected in series, the total resistance adds up to 15 ohms. this causes a current of 0.8 amperes to flow through the circuit. the voltage drop across the 5-ohm resistor is 4 volts, and across the 10-ohm resistor is 8 volts. so, the total potential difference between the starting point (a) and the endpoint (b) is 12 volts, matching the battery’s output.

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