**The power dissipated in circuit A is twice the power dissipated in circuit B.****The current through the resistor is the same for circuits A and C.****The current through the resistor is the same for circuits A and B.****The voltage at one resistor in circuit C is twice the voltage at one resistor in circuit B.****The total energy dissipated in circuit C is twice the total energy dissipated in circuit B.**

The **question aims** to answer statements about the three circuits given above. **Difference** between potential in two points in an electric field, which helps current to flow in the circuits, is called **voltage** (V). **The term current** is defined as the rate of flow of electrons in the circuit.

**Expert Answer**

**Part(a)**

**Yes, the statement $(a)$ is true.** The **energy dissipated in circuit** $A$ is twice as large as in-circuit $B$. The current though $A$ is twice as much as the current to $B$, so it provides a dispersed power twice the size, assuming that both circuits have the same power source.

**Part(b)**

**Yes, statement $(b)$ is correct.** **Circuit $C$ is a different type of circuit compared** to $A$. The current through resistors is the same; however, for each circuit, the current need for the source in each circuit is different. Circuit $A$ requires $\dfrac{1}{2}$ of the current in the source compared to its $C$ counterpart.

For circuit $A$, current is calculated by using following procedure.

\[I=\dfrac{V}{R}\]

Let’s suppose $V=10v$ and $R=1\Omega$

\[I=\dfrac{10}{1}=10 A\]

For circuit $C$, the **current is calculated by using the following procedure**. There are two branches, so there are two values of current.

\[I_{1}=\dfrac{V}{R_{1}}\]

\[I_{2}=\dfrac{V}{R_{2}}\]

Let’s suppose $V=10v$, $R_{1}=1\Omega$ and $R_{2}=1\Omega$

\[I_{1}=\dfrac{10}{1}=10 A\]

\[I_{2}=\dfrac{10}{1}=10 A\]

\[I=I_{1}+I_{2}\]

\[I=20A\]

The **current in the resistor is the same in both circuits**, but the overall current is different.

**Part(c)**

**Yes, the statement is correct.** In circuit $B$, the current flow is the same in each resistor in the circuit, and in this case, since they are the same resistance, the voltage through each resistor is $\dfrac{1}{2}V$.

**Part(d)**

**Yes, the statement is correct.**** Voltage** along a single resistor in circuit $C$ is twice as compared to circuit $B$. Circuit $B$ is a series circuit, so **voltage divides across two resistors.**

**Part(e)**

**Yes, the $IV$ current strength in $C$ is twice as high as the current in $B$. So, the statement is correct.**

**Numerical Result**

(a) The statement is** correct**.

(b) The statement is **correct.**

(c) The statement is **correct.**

(d) The statement is **correct.**

(e) The statement is **correct.**

**Example**

**Consider the two circuits shown below. All resistors and all batteries are the same. Which statements are true and which are false?**

**– The energy dissipated in circuit $B$ is twice the force dissipated in circuit $A$.**

**Solution**

**No, statement $(a)$ is not true**. The **energy dissipated in circuit** $A$ is twice as large as in-circuit $B$. The **current** through $A$ is twice as much as the current to $B$, so it provides a dispersed power twice the size, assuming that both circuits have the same power source. **Hence, the statement is not true.**

*Images/Mathematical drawings are created with Geogebra.*