$(a)$ Calculate the resistance of the wire using the graph.
$(b)$ How many $176 \,\Omega$ resistors in parallel are required to carry $5\, A$ on a $220\, V$ line?
$(c)$ Define electric power. Derive the relation between power,potential difference,and resistance.
$(b)$ How many $176 \,\Omega$ resistors in parallel are required to carry $5\, A$ on a $220\, V$ line?
$(c)$ Define electric power. Derive the relation between power,potential difference,and resistance.
(N/A) The resistance $R$ is given by Ohm's law: $R = V / I$.
From the graph,at $V = 2 \, V$,the current $I = 0.1 \, A$.
Therefore,$R = 2 \, V / 0.1 \, A = 20 \, \Omega$.
$(b)$ Given: Total current $I = 5 \, A$,Voltage $V = 220 \, V$.
The required total resistance $R_{eq}$ of the circuit is $R_{eq} = V / I = 220 \, V / 5 \, A = 44 \, \Omega$.
Let $n$ resistors of $176 \, \Omega$ each be connected in parallel.
The equivalent resistance for $n$ resistors in parallel is $1 / R_{eq} = n / R$.
$1 / 44 = n / 176$.
$n = 176 / 44 = 4$.
Thus,$4$ resistors are required.
$(c)$ Electric power is defined as the rate at which electric energy is dissipated or consumed in an electric circuit.
We know that power $P = W / t$ and work done $W = V \cdot I \cdot t$.
So,$P = (V \cdot I \cdot t) / t = V \cdot I$.
From Ohm's law,$I = V / R$.
Substituting $I$ in the power equation: $P = V \cdot (V / R) = V^2 / R$.
From the graph,at $V = 2 \, V$,the current $I = 0.1 \, A$.
Therefore,$R = 2 \, V / 0.1 \, A = 20 \, \Omega$.
$(b)$ Given: Total current $I = 5 \, A$,Voltage $V = 220 \, V$.
The required total resistance $R_{eq}$ of the circuit is $R_{eq} = V / I = 220 \, V / 5 \, A = 44 \, \Omega$.
Let $n$ resistors of $176 \, \Omega$ each be connected in parallel.
The equivalent resistance for $n$ resistors in parallel is $1 / R_{eq} = n / R$.
$1 / 44 = n / 176$.
$n = 176 / 44 = 4$.
Thus,$4$ resistors are required.
$(c)$ Electric power is defined as the rate at which electric energy is dissipated or consumed in an electric circuit.
We know that power $P = W / t$ and work done $W = V \cdot I \cdot t$.
So,$P = (V \cdot I \cdot t) / t = V \cdot I$.
From Ohm's law,$I = V / R$.
Substituting $I$ in the power equation: $P = V \cdot (V / R) = V^2 / R$.
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