Calculations on the Whole Circuit
Exercise. A 3 V battery is connected to two resistors in series. The resistances of the resistors are 10 Ω and 20 Ω. Find the potential difference across each resistor.
Answer. Let us call the 10 Ω resistor R1 and the 20 Ω resistor R2.
First, find the current using Ohm's law V = IR. The combined resistance is R = 10 + 20 = 30 Ω. So the current is I = V/R = 3/30 = 0.1 A.
Next, find the potential difference across one resistor, again using Ohm's law.
The potential difference across R1 is V1 = IR1 = 0.1 x 10 = 1 V.
We know that the sum of the potential difference across each resistor is equal to the potential difference across both resistors. So potential difference across R2 is V2 = V - V1 = 3 - 1 = 2 V.
Exercise. A 3 V battery is connected to two resistors in parallel. The resistances of the resistors are 10 Ω and 20 Ω. Find the current through the battery.
Answer. The potential difference across each resistor is the same. So potential difference across R1 is 3 V. Potential difference across R2 is also 3 V.
So we can find the current in R1 using Ohm's law. It is I1 = V/R1 = 3/10 = 0.3 A.
We can find the current in R2 in the same way: I2 = V/R1 = 3/20 = 0.15 A.
These two currents recombine and go back to the battery. The current through the battery is the sum of these currents: 0.3 + 0.15 = 0.45 A.