The circuit shows a battery of negligible internal resistance connected to three resistors. (a) Calculate the potential difference across the 15 resistor. (b) Calculate the current I1 in the 4.0 resistor. (c) Calculate the current I2 and the resistance R.

Sawa Jozee, hebu tusuluhishe tena.

Swali la 1:

a) Kokotoa tofauti ya uwezo (potential difference) kwenye kipingamizi cha $15 \, \Omega$.

Step 1: Tumia Sheria ya Ohm, $V = IR$. Mkondo wa umeme unaopita kwenye kipingamizi cha $15 \, \Omega$ ni $0.24 \, \text{A}$. $V = 0.24 \, A \times 15 \, \Omega$ $V = 3.6 \, \text{V}$ Tofauti ya uwezo kwenye kipingamizi cha $15 \, \Omega$ ni $\boxed{3.6 V}$.

b) Kokotoa mkondo wa umeme $I_1$ kwenye kipingamizi cha $4.0 \, \Omega$.

Step 1: Tofauti ya uwezo kwenye vipingamizi vilivyounganishwa sambamba ($R$ na $15 \, \Omega$) ni sawa na $3.6 \, \text{V}$ (kutoka sehemu a). Jumla ya tofauti ya uwezo kutoka betri ni $6.0 \, \text{V}$. Tofauti ya uwezo kwenye kipingamizi cha $4.0 \, \Omega$ ni $V_{4.0\Omega}$. Kwa mzunguko wa mfululizo, $V_{total} = V_{4.0\Omega} + V_{parallel}$. $6.0 \, V = V_{4.0\Omega} + 3.6 \, \text{V}$ $V_{4.0\Omega} = 6.0 \, V - 3.6 \, \text{V}$ $V_{4.0\Omega} = 2.4 \, \text{V}$

Step 2: Tumia Sheria ya Ohm kukokotoa $I_1$. $I_1 = \frac{V_{4.0\Omega}}{R_{4.0\Omega}}$ $I_1 = \frac{2.4 \, V}{4.0 \, \Omega}$ $I_1 = 0.6 \, \text{A}$ Mkondo wa umeme $I_1$ ni $\boxed{0.6 A}$.

c) Kokotoa mkondo wa umeme $I_2$ na kipingamizi $R$.

Step 1: Kokotoa mkondo wa umeme $I_2$ kwa kutumia Sheria ya Kirchhoff ya Mikondo. Mkondo wa umeme $I_1$ hugawanyika kuwa $I_2$ na $0.24 \, \text{A}$. $I_1 = I_2 + 0.24 \, \text{A}$ $0.6 \, A = I_2 + 0.24 \, \text{A}$ $I_2 = 0.6 \, A - 0.24 \, \text{A}$ $I_2 = 0.36 \, \text{A}$ Mkondo wa umeme $I_2$ ni $\boxed{0.36 A}$.

Step 2: Kokotoa kipingamizi $R$. Kipingamizi $R$ kimeunganishwa sambamba na kipingamizi cha $15 \, \Omega$, hivyo tofauti ya uwezo kwenye $R$ ni $3.6 \, \text{V}$. Tumia Sheria ya Ohm: $R = \frac{V}{I_2}$. $R = \frac{3.6 \, V}{0.36 \, A}$ $R = 10 \, \Omega$ Kipingamizi $R$ ni $\boxed{10 \Omega}$.

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