The current through each resistor in the two-resistor circuit is the current through the resistor in the one-resistor circuit (the circuit in Part A). The voltage across each resistor in the two-resistor circuit is the voltage across the resistor in the one-resistor circuit. a. the same as / half
b. half / half
c. twice / half
d. half / twice
e. half / the same as
f. twice / twice

Option C is correct

Twice/half

Explanation:

Let assume the resistor have the same resistance. i.e R1=R2=R

The current in a two resistor series circuit is the same, series connection has same current.

Req for series connection is

Req=R1+R2=R+R=2R

Then using ohms law

V=IReq

I=V/Req

I=V/2R

If we reduce the current to one resistor and also let assume they have the same resistance, then the current will be double in this case.

Using ohms law

V=IR,

In this case it has one resistor and the Req is R

Then, I=V/R, which is twice of the first.

Since the same voltage is flow through the same circuit

Then for the two resistor circuit

V=IReq

Then, V=I×2R

V=2IR

Now, if we reduce resistor to 1,

Then the Req=R,

So using ohms law still

V=IReq

V=IR

We notice that the voltage is reduce to half of the initial.

So the answer is twice and half

Option C is correct

b. half / half

Explanation:

Lets understand this problem with a simple example, we will suppose a simple series circuit in this example.

Example:

Consider a simple circuit where a single resistor of value 1 Ω is connected with a voltage source of 10 V.

The current in the circuit is

I = V/R = 10/1 = 10 A

The voltage across resistor is

V = IR = 10*1 = 10 V

Now consider a circuit where two resistors of value 1 Ω each are connected in series with a voltage source of 10 V.

The current in the circuit is

I = V/R = 10/2 = 5 A

The voltage across each resistor is

V = IR = 5*1 = 5 V

Conclusion:

So the current in two-resistor circuit is 5 A as compared to the current in one-resistor circuit of 10 A which means that current is reduced to half.

The voltage across each resistor in the two-resistor circuit is 5 V as compared to the voltage across the one-resistor circuit of 10 V which means that the voltage is reduced to half.

So the correct option is b. half and half.

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